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Automatic Control, IEEE Transactions on

Issue 6 • Date June 2014

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Displaying Results 1 - 25 of 36
  • Table of contents

    Page(s): C1 - C4
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  • IEEE Transactions on Automatic Control publication information

    Page(s): C2
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  • Scanning the issue

    Page(s): 1393 - 1394
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  • Lyapunov-Based Small-Gain Theorems for Hybrid Systems

    Page(s): 1395 - 1410
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    Constructions of strong and weak Lyapunov functions are presented for a feedback connection of two hybrid systems satisfying certain Lyapunov stability assumptions and a small-gain condition. The constructed strong Lyapunov functions can be used to conclude input-to-state stability (ISS) of hybrid systems with inputs and global asymptotic stability (GAS) of hybrid systems without inputs. In the absence of inputs, we also construct weak Lyapunov functions nondecreasing along solutions and develop a LaSalle-type theorem providing a set of sufficient conditions under which such functions can be used to conclude GAS. In some situations, we show how average dwell time (ADT) and reverse average dwell time (RADT) “clocks” can be used to construct Lyapunov functions that satisfy the assumptions of our main results. The utility of these results is demonstrated for the “natural” decomposition of a hybrid system as a feedback connection of its continuous and discrete dynamics, and in several design-oriented contexts: networked control systems, event-triggered control, and quantized feedback control. View full abstract»

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  • Youla-Like Parametrizations Subject to QI Subspace Constraints

    Page(s): 1411 - 1422
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    Consider that a linear time-invariant (LTI) plant is given and that we wish to design a stabilizing controller for it. Admissible controllers are LTI and must belong to a pre-selected subspace that may impose structural restrictions, such as sparsity constraints. The subspace is assumed to be quadratically invariant (QI) with respect to the plant, which, from prior results, guarantees that there is a convex parametrization of all admissible stabilizing controllers provided that an initial admissible stable stabilizing controller is provided. This paper addresses the previously unsolved problem of extending Youla's classical parametrization so that it admits QI subspace constraints on the controller. In contrast with prior parametrizations, the one proposed here does not require initialization and it does not require the existence of a stable stabilizing controller. The main idea is to cast the stabilizability constraint as an exact model-matching problem with stability restrictions, which can be tackled using existing methods. Furthermore, we show that, when it exists, the solution of the exact model-matching problem can be used to compute an admissible stabilizing controller. Applications of the proposed parametrization on the design of norm-optimal controllers via convex methods are also explored. An illustrative example is provided, and a special case is discussed for which the exact model matching problem has a unique and easily computable solution. View full abstract»

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  • Online Markov Decision Processes With Kullback–Leibler Control Cost

    Page(s): 1423 - 1438
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    This paper considers an online (real-time) control problem that involves an agent performing a discrete-time random walk over a finite state space. The agent's action at each time step is to specify the probability distribution for the next state given the current state. Following the setup of Todorov, the state-action cost at each time step is a sum of a state cost and a control cost given by the Kullback-Leibler (KL) divergence between the agent's next-state distribution and that determined by some fixed passive dynamics. The online aspect of the problem is due to the fact that the state cost functions are generated by a dynamic environment, and the agent learns the current state cost only after selecting an action. An explicit construction of a computationally efficient strategy with small regret (i.e., expected difference between its actual total cost and the smallest cost attainable using noncausal knowledge of the state costs) under mild regularity conditions is presented, along with a demonstration of the performance of the proposed strategy on a simulated target tracking problem. A number of new results on Markov decision processes with KL control cost are also obtained. View full abstract»

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  • Distributed RHC for Tracking and Formation of Nonholonomic Multi-Vehicle Systems

    Page(s): 1439 - 1453
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    This paper considers the synchronous distributed receding horizon control (RHC) for a general problem of the nonholonomic multi-vehicle systems, i.e., the simultaneous forward/backward tracking, regulation and formation with the collision avoidance. First, for each vehicle, a positively invariant terminal-state region and an auxiliary controller are developed. When every vehicle lies in its terminal-state region, all the distributed control targets are achieved by the auxiliary controller. Second, the compatibility constraint, restricting the norm of the uncertain deviation between the assumed and actual predictive trajectories of each vehicle, is given, which respects both the collision avoidance and convergence guarantee. Thirdly, a robust collision avoidance constraint tolerating for the uncertain deviation is designed. By these designs, an overall control algorithm is proposed, by applying which all the control targets are achieved. Two illustrative examples are provided to show the advantage and effectiveness of the proposed approach. View full abstract»

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  • Secure Estimation and Control for Cyber-Physical Systems Under Adversarial Attacks

    Page(s): 1454 - 1467
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    The vast majority of today's critical infrastructure is supported by numerous feedback control loops and an attack on these control loops can have disastrous consequences. This is a major concern since modern control systems are becoming large and decentralized and thus more vulnerable to attacks. This paper is concerned with the estimation and control of linear systems when some of the sensors or actuators are corrupted by an attacker. We give a new simple characterization of the maximum number of attacks that can be detected and corrected as a function of the pair (A,C) of the system and we show in particular that it is impossible to accurately reconstruct the state of a system if more than half the sensors are attacked. In addition, we show how the design of a secure local control loop can improve the resilience of the system. When the number of attacks is smaller than a threshold, we propose an efficient algorithm inspired from techniques in compressed sensing to estimate the state of the plant despite attacks. We give a theoretical characterization of the performance of this algorithm and we show on numerical simulations that the method is promising and allows to reconstruct the state accurately despite attacks. Finally, we consider the problem of designing output-feedback controllers that stabilize the system despite sensor attacks. We show that a principle of separation between estimation and control holds and that the design of resilient output feedback controllers can be reduced to the design of resilient state estimators. View full abstract»

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  • Quickest Detection of a Random Pulse in White Gaussian Noise

    Page(s): 1468 - 1479
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    A class of stochastic processes characterized by rapid transitions in their structure is considered and the quickest detection of such transitions is studied in a Bayesian framework. The emphasis is on stochastic processes consisting of a randomly arrived causal pulse (possibly with a set of random parameters such as amplitude and duration) and an additive white Gaussian noise. In this model, the pulse shape and the prior joint density of the arrival time and other random parameters are assumed known. The task of quickest detection in this paper is described mathematically by minimizing the expected detection error. The detection error is represented by a nonlinear function of the distance between the actual transition time and its associated detection time. The assumptions on this function are fairly mild and allow to flexibly design its shape for a desired trade-off between the detection delay and the false alarm rate. Two special cases of such design are well known error measures: mean squared and mean absolute error. The quickest detection problem-a subclass of optimal stopping time problems-is formulated as a stochastic optimal control problem and is resolved using dynamic programming. The optimal detection rule is determined in terms of the solution of an integral equation that cannot be directly solved due to its complexity. This equation is later used to develop a class of suboptimal detection rules and a lower bound on the minimum error. Using this lower bound, it is shown for a numerical example that the suboptimal detector is nearly optimal. View full abstract»

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  • Minimizing Convergence Error in Multi-Agent Systems Via Leader Selection: A Supermodular Optimization Approach

    Page(s): 1480 - 1494
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    In a leader-follower multi-agent system (MAS), the leader agents act as control inputs and influence the states of the remaining follower agents. The rate at which the follower agents converge to their desired states, as well as the errors in the follower agent states prior to convergence, are determined by the choice of leader agents. In this paper, we study leader selection in order to minimize convergence errors experienced by the follower agents, which we define as a norm of the distance between the follower agents' intermediate states and the convex hull of the leader agent states. By introducing a novel connection to random walks on the network graph, we show that the convergence error has an inherent supermodular structure as a function of the leader set. Supermodularity enables development of efficient discrete optimization algorithms that directly approximate the optimal leader set, provide provable performance guarantees, and do not rely on continuous relaxations. We formulate two leader selection problems within the supermodular optimization framework, namely, the problem of selecting a fixed number of leader agents in order to minimize the convergence error, as well as the problem of selecting the minimum-size set of leader agents to achieve a given bound on the convergence error. We introduce algorithms for approximating the optimal solution to both problems in static networks, dynamic networks with known topology distributions, and dynamic networks with unknown and unpredictable topology distributions. Our approach is shown to provide significantly lower convergence errors than existing random and degree-based leader selection methods in a numerical study. View full abstract»

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  • Optimal Power Management in Wireless Control Systems

    Page(s): 1495 - 1510
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    This paper considers the control of a linear plant when plant state information is being transmitted from a sensor to the controller over a wireless fading channel. The power allocated to these transmissions determines the probability of successful packet reception and is allowed to adapt online to both channel conditions and plant state. The goal is to design plant input and transmit power policies that minimize an infinite horizon cost combining power expenses and the conventional linear quadratic regulator control cost. Since plant inputs and transmit powers are in general coupled, a restricted information structure is imposed allowing them to be designed separately. Under this information structure the standard LQR controller becomes the optimal plant input policy, while the optimal communication policy follows a Markov decision process minimizing transmit power at the sensor and state estimation error at the controller. The optimal power adaptation to channel and plant states is examined qualitatively for general forward error correcting codes. In the particular case of capacity achieving codes event-triggered policies are recovered, where the sensor decides whether to transmit or not based on plant and channel conditions. Approximate dynamic programming is employed to derive a family of tractable suboptimal communication policies exhibiting the same qualitative features as the optimal one. The performance of our suboptimal policies is shown in simulations and is contrasted to other simple transmission policies. View full abstract»

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  • Stability Analysis of A Class of Hybrid Stochastic Retarded Systems Under Asynchronous Switching

    Page(s): 1511 - 1523
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    The stability of a class of hybrid stochastic retarded systems (HSRSs) with an asynchronous switching controller is investigated. In this model, the controller design relies on the observed jumping parameters, which are however delayed and thus can not be measured in real-time precisely. This delayed time interval, referred to as the “asynchronous switching interval”, is Markovian and dependent on the actual switching signal. The sufficient conditions under which the system is either stochastically asymptotic stable or input-to-state stable are obtained by applying the extended Razumikhin-type theorem to the asynchronous switching interval. These results are less conservative as it is only required that the designed Lyapunov function is non-decreasing. It is shown that the stability of the considered system can be guaranteed by a sufficiently small mode transition rate of the underlying Markov process, which is a conclusion similar to that in asynchronous deterministic switched systems. The effectiveness and correctness of the obtained results are finally verified by a numerical example. View full abstract»

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  • Distributed Constrained Optimization by Consensus-Based Primal-Dual Perturbation Method

    Page(s): 1524 - 1538
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    Various distributed optimization methods have been developed for solving problems which have simple local constraint sets and whose objective function is the sum of local cost functions of distributed agents in a network. Motivated by emerging applications in smart grid and distributed sparse regression, this paper studies distributed optimization methods for solving general problems which have a coupled global cost function and have inequality constraints. We consider a network scenario where each agent has no global knowledge and can access only its local mapping and constraint functions. To solve this problem in a distributed manner, we propose a consensus-based distributed primal-dual perturbation (PDP) algorithm. In the algorithm, agents employ the average consensus technique to estimate the global cost and constraint functions via exchanging messages with neighbors, and meanwhile use a local primal-dual perturbed subgradient method to approach a global optimum. The proposed PDP method not only can handle smooth inequality constraints but also non-smooth constraints such as some sparsity promoting constraints arising in sparse optimization. We prove that the proposed PDP algorithm converges to an optimal primal-dual solution of the original problem, under standard problem and network assumptions. Numerical results illustrating the performance of the proposed algorithm for a distributed demand response control problem in smart grid are also presented. View full abstract»

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  • Tracking Control for Nonlinear Networked Control Systems

    Page(s): 1539 - 1554
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    We investigate the tracking control of nonlinear networked control systems (NCS) affected by disturbances. We consider a general scenario in which the network is used to ensure the communication between the controller, the plant and the reference system generating the desired trajectory to be tracked. The communication constraints induce non-vanishing errors (in general) on the feedforward term and the output of the reference system, which affect the convergence of the tracking error. As a consequence, available results on the stabilization of equilibrium points for NCS are not applicable. Therefore, we develop an appropriate hybrid model and we give sufficient conditions on the closed-loop system, the communication protocol and an explicit bound on the maximum allowable transmission interval guaranteeing that the tracking error converges to the origin up to some errors due to both the external disturbances and the aforementioned non-vanishing network-induced errors. The results cover a large class of the so-called uniformly globally asymptotically stable protocols which include the well-known round-robin and try-once-discard protocols. We also introduce a new dynamic protocol suitable for tracking control. Finally, we show that our approach can be used to derive new results for the observer design problem for NCS. It has to be emphasized that the approach is also new for the particular case of sampled-data systems. View full abstract»

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  • Compensation of Wave Actuator Dynamics for Nonlinear Systems

    Page(s): 1555 - 1570
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    The problem of stabilization of PDE-ODE cascades has been solved in the linear case for several PDE classes, whereas in the nonlinear case the problem has been solved only for the transport/delay PDE, namely for compensation of an arbitrary delay at the input of a nonlinear plant. Motivated by a specific engineering application in off-shore drilling, we solve the problem of stabilization of the cascade of a wave PDE with a general nonlinear ODE. Due to the presence of nonlinearities of arbitrary growth and the time-reversibility of the wave PDE, and due to the possibility of using arguments based on Lyapunov functionals or explicit solutions, several stability analysis approaches are possible. We present stability results in the H2 × H1 and C1 × C0 norms for general nonlinear ODEs, as well as in the H1 × L2 norm for linear ODEs. We specialize our general design for wave PDE-ODE cascades to the case of a wave PDE whose uncontrolled end does not drive an ODE but is instead governed by a nonlinear Robin boundary condition (a “nonlinear spring,” as in the friction law in drilling). This is the first global stabilization result for wave equations that incorporate non-collocated destabilizing nonlinearities of superlinear growth. We present two numerical examples, one with a nonlinear ODE and one with a nonlinear spring at the uncontrolled boundary of the wave PDE. View full abstract»

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  • Consensus of Networked Mechanical Systems With Communication Delays: A Unified Framework

    Page(s): 1571 - 1576
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    This technical note addresses the consensus problem of networked uncertain mechanical systems which interact on directed graphs containing a spanning tree and are subjected to nonuniform communication delays. The challenge lies in the unclear input-output property of a linear networked system containing communication delays and the unclear convergent property of this system under an external input. We establish a new input-output property of this linear networked system and moreover its convergent property under an external input, upon which, we establish a unified framework to resolve the consensus problem of multiple mechanical systems. The proposed consensus framework unifies/extends the existing results and in addition yields a fully cascaded closed-loop system. With Lyapunov-like analysis and frequency domain input-output analysis, we show that the proposed unified consensus control scheme ensures consensus without the integral action of the sliding vector, and scaled weighted average consensus with the integral action of the sliding vector. Simulation results are provided to demonstrate the performance of the proposed consensus schemes. View full abstract»

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  • Robust Stabilization of the Generalized Triangular Form Nonlinear Systems With Disturbances

    Page(s): 1577 - 1582
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    We investigate the problem of global uniform input-to-state stabilization of nonlinear generalized triangular form (GTF) control systems of ODE with time-varying and periodic dynamics and with external essentially bounded disturbances. Our first main result is a statement which is a kind of extension of theorems on “adding an integrator” to the case of input-to-state stabilization of GTF systems. As a corollary we immediately obtain our second main result on global uniform input-to-state stabilzation of GTF systems w.r.t. the external disturbances. The latter is a generalization of the recent result, devoted to the global asymptotic stabilization of the GTF systems without disturbances. It is essential that the proof of the main result is based on the converse ISS Lyapunov theorems for the time-varying systems, which allows to simplify construction proposed our recent work. View full abstract»

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  • Optimal Placement of Marine Protected Areas: a Trade-off Between Fisheries Goals and Conservation Efforts

    Page(s): 1583 - 1587
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    Marine Protected Areas (MPAs) are regions in the ocean or along coastlines where fishing is controlled to avoid the reduction or elimination of fish populations. A central question is where exactly to establish an MPA. We cast this as an optimal problem along a one-dimensional coast-line, where fish are assumed to move diffusively, and are subject to recruitment, natural death and harvesting through fishing. The functional being maximized is a weighted sum of the average fish density and the average fishing yield. It is shown that optimal controls exist, and that the location of the MPA is determined by two key model parameters, namely the size of the coast, and the weight of the average fish density in the functional. View full abstract»

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  • Robust Sinusoid Identification With Structured and Unstructured Measurement Uncertainties

    Page(s): 1588 - 1593
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    In this note a globally stable methodology is proposed to estimate the frequency, phase, and amplitude of a sinusoidal signal affected by additive structured and bounded unstructured disturbances. The structured disturbances belong to the class of time-polynomial signals incorporating both bias and drift phenomena. Stability and robustness results are given by resorting to Input-to-State stability arguments. Simulation comparative results show the effectiveness of the proposed technique. View full abstract»

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  • Exponential Stability of Homogeneous Positive Systems of Degree One With Time-Varying Delays

    Page(s): 1594 - 1599
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    While the asymptotic stability of positive linear systems in the presence of bounded time delays has been thoroughly investigated, the theory for nonlinear positive systems is considerably less well-developed. This technical note presents a set of conditions for establishing delay-independent stability and bounding the decay rate of a significant class of nonlinear positive systems which includes positive linear systems as a special case. Specifically, when the time delays have a known upper bound, we derive necessary and sufficient conditions for exponential stability of: a) continuous-time positive systems whose vector fields are homogeneous and cooperative and b) discrete-time positive systems whose vector fields are homogeneous and order-preserving. We then present explicit expressions that allow us to quantify the impact of delays on the decay rate and show that the best decay rate of positive linear systems that our bounds provide can be found via convex optimization. Finally, we extend the results to general linear systems with time-varying delays. View full abstract»

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  • On Weak-Invariance Principles for Nonlinear Switched Systems

    Page(s): 1600 - 1605
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    In this technical note, we develop two weak-invariance principles for nonlinear switched systems. We first present a union weak-invariance principle for switched systems which includes as a special case the integral invariance principle. It is shown that the switched solution approaches the largest weakly invariant set of the combined zero loci of the output functions. Then, we extend the union weak-invariance principle to an intersection weak-invariance principle, which greatly reduces the convergence region. Unlike the existing results, in which the constructions of Lyapunov functions are inevitable, our principles do not require the existence of Lyapunov functions. Numerical examples are presented to demonstrate the feasibility of our principles, as well as applications to multi-agent consensus problems. View full abstract»

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  • Stability of Prioritized Scheduling Policies in Manufacturing Systems With Setup Times

    Page(s): 1606 - 1611
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    We study the dynamic scheduling of a multi-item machine with setup times and static priorities. We consider a class of base-stock policies for this system and seek sharp stability conditions that allow us to respect the item priorities over a large region of the decision space. We show that requiring the existence of a linear Lyapunov function that decreases between production runs reduces to an intuitive stability condition, which can nevertheless be too conservative for this policy class. We then sharpen this result by showing that, if the original condition is satisfied for the highest-priority N-1 part types, the system with N items is stable. Finally, we develop stability conditions based on affine Lyapunov functions. View full abstract»

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  • Jointly Optimal LQG Quantization and Control Policies for Multi-Dimensional Systems

    Page(s): 1612 - 1617
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    For controlled Rn-valued linear systems driven by Gaussian noise under quadratic cost criteria, we investigate the existence and the structure of optimal quantization and control policies. For fully observed and partially observed systems, we establish the global optimality of a class of predictive encoders and show that an optimal quantization policy exists, provided that the quantizers allowed are ones which have convex codecells. Furthermore, optimal control policies are linear in the conditional estimate of the state, and a form of separation of estimation and control holds. View full abstract»

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  • Robust Static Output Feedback Controllers via Robust Stabilizability Functions

    Page(s): 1618 - 1623
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    This technical note addresses the design of robust static output feedback controllers that minimize a polynomial cost and robustly stabilize a system with polynomial dependence on an uncertain vector constrained in a semialgebraic set. The admissible controllers are those in a given hyper-rectangle for which the system is well-posed. First, the class of robust stabilizability functions is introduced, i.e., the functions of the controller that are positive whenever the controller robustly stabilizes the system. Second, the approximation of a robust stabilizability function with a controller-dependent lower bound is proposed through a sums-of-squares (SOS) program exploiting a technique developed in the estimation of the domain of attraction. Third, the derivation of a robust stabilizing controller from the found controller-dependent lower bound is addressed through a second SOS program that provides an upper bound of the optimal cost. The proposed method is asymptotically non-conservative under mild assumptions. View full abstract»

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  • Robust Adaptive Control for a Class of MIMO Nonlinear Systems by State and Output Feedback

    Page(s): 1624 - 1629
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    In this technical note, high dimensional integral Lyapunov functions are introduced for a class of MIMO nonlinear systems with unknown nonlinearities. First, adaptive state feedback control is presented based on the integral Lyapunov function. When only the output is measurable, by using a high-gain observer to estimate the derivative of the system output, adaptive output feedback control is also derived. The proposed control scheme provides a general approach to stabilize the MIMO plant without any restrictive assumptions. The control is continuous and ensures closed-loop stability and convergence of the tracking error to a small residual set. The size of the tracking error at steady state can be specified a priori and guaranteed by choosing the design parameters. View full abstract»

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Aims & Scope

In the IEEE Transactions on Automatic Control, the IEEE Control Systems Society publishes high-quality papers on the theory, design, and applications of control engineering.  Two types of contributions are regularly considered

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Meet Our Editors

Editor-in-Chief
P. J. Antsaklis
Dept. Electrical Engineering
University of Notre Dame