Abstract
Model uncertainties are usually unavoidable in the control systems, which are caused by imperfect system modeling, disturbances, and nonsmooth dynamics. This paper presents a novel method to address the robust control problem for uncertain systems. The original robust control problem of the uncertain system is first transformed into an optimal control of nominal system via selecting the appropriate cost function. Then, we develop an adaptive critic leaning algorithm to learn online the optimal control solution, where only the critic neural network (NN) is used, and the actor NN widely used in the existing methods is removed. Finally, the feasibility analysis of the control algorithm is given in the paper. Simulation results are given to show the availability of the presented control method.
Highlights
Based on the above facts, we develop an adaptive critic learning algorithm to resolve the robust control problem of uncertain systems
We construct an equivalence between the robust control problem and the optimal control problem via selecting the appropriate cost function; a single critic neural network (NN) is used to reformulate the cost function
To realize the optimal control solution, we design an adaptive critic leaning algorithm; since it has strong convergence, the actor NN widely used in existing ADP results is removed
Summary
A continuous-time (CT) uncertain system can be written as x_(t) f(x) + g(x)(u + b(x)u) + g(x)d(x), (1). E purpose of this paper is designing a controller to make system (1) asymptotically stable under the uncertainties b(x) and d(x). To this end, we give following assumptions. Zx en, we will give the lemma to explain the robust control problem of system (1) which can be transformed into an optimal control problem of system (2) via constructing cost function (3). Assume that the solution can be solved via optimal control problem of system (2) with cost function (3) and d2max(x) ≥ dT(x)N d(x), and this solution can make uncertain system (1) asymptotically stable, which means that the optimal control solution is the solution of the robust control problem for system (1). If the controller exists, we can say the uncertain system is robustly stable
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