Optimal Control of Time Varying Linear Systems: Neural Networks

Using the principle of parsimony, some interesting systems are modeled as linear systems. In some applications, assumption of time invariance of the system is too restrictive. Thus there are many applications where linear time varying systems naturally arise as the models of system dynamics. There are several formulations of optimal control of linear time-varying systems. For instance, time optimal control is well studied. We formulate an interesting optimal control problem for time varying linear systems. First we consider a discrete time system. The state space description of such discrete time, linear time varying system is given by X (k+1) = A (k) X (k) + B (k) U (k) and Y (k) = C (k) X (k) + D (k) U (k). We consider the case where D (k) = 0 for all 'k'. We consider a multi-input, multi-output linear time varying system. The solution can easily be generalized to Continuous Time Linear Time Varying Systems. Briefly Stochastic version of the problem is discussed.