Filter-Free Parameter Estimation Method for Continuous-Time Systems

Existing parameter estimation methods for continuous-time systems (CTSs) primarily filter the signal and transform differential equations into linear regression equations (LREs); therefore, the estimation method for LREs can be used. However, these methods have the following limitations. First, the convergence speed of parameter estimation is low because of the filtering process; second, these methods require the system input to satisfy a persistent excitation (PE) condition, which is difficult in practical applications; third, these methods cannot estimate fast-changing time-varying parameters. To overcome these drawbacks, a new parameter estimation method for CTSs is proposed in this study, without adding a filter; thus, the proposed method has a much faster convergence rate. Furthermore, the PE condition is removed such that the system states converge to constant values. This method can quickly identify the time-varying parameters, removing the key assumption that the first derivative of the parameter is bounded. Finally, the effectiveness of the method is verified through numerical simulations
Note to Practitioners
—In many practical applications, the unknown parameters of a system must be estimated before realizing its specific control objectives. For continuous-time systems, most of the traditional parameter estimation methods need to filter the system signal first, which increases the computational complexity. Moreover, to ensure convergence of the estimation schemes, certain excitation conditions such as the persistent excitation condition are required for the input signal. However, these conditions may be difficult to satisfy in practice. Furthermore, the system output will continuously oscillate as the dynamics proceed if the input signals are excited by a random variable; however, most tracking problems require the output signal to converge precisely to a fixed objective. In addition, the filter can reduce the convergence speed for traditional estimation algorithms; thus, the time-varying parameters of these parameters are very difficult for algorithms to estimate. All these problems are well addressed by the proposed filter-free parameter estimation method. Using the proposed method, practitioners can realize the joint objective of precise tracking and parameter estimation concurrently; meanwhile, the convergence speed is also significantly enhanced. The strongly time-varying unknown parameters can be estimated as well, which makes the method attractive for practical applications.