Optimal Guaranteed Cost Control Problem Research Articles

Optimal Guaranteed Cost Sliding Mode Control for Constrained-Input Nonlinear Systems With Matched and Unmatched Disturbances

Based on integral sliding mode and approximate dynamic programming (ADP) theory, a novel optimal guaranteed cost sliding mode control is designed for constrained-input nonlinear systems with matched and unmatched disturbances. When the system moves on the sliding surface, the optimal guaranteed cost control problem of sliding mode dynamics is transformed into the optimal control problem of a reformulated auxiliary system with a modified cost function. The ADP algorithm based on single critic neural network (NN) is applied to obtain the approximate optimal control law for the auxiliary system. Lyapunov techniques are used to demonstrate the convergence of the NN weight errors. In addition, the derived approximate optimal control is verified to guarantee the sliding mode dynamics system to be stable in the sense of uniform ultimate boundedness. Some simulation results are presented to verify the feasibility of the proposed control scheme.

Optimal guaranteed cost control of uncertain non‐linear systems using adaptive dynamic programming with concurrent learning

In this study, the authors study the optimal guaranteed cost control problem for a class of non-linear uncertain systems based on adaptive dynamic programming (ADP) with concurrent learning. A neural network-based approximate optimal guaranteed cost control design is developed not only to ensure the system stability for all admissible uncertainties but also to achieve a minimal guaranteed cost. First, the optimal guaranteed cost control problem is transformed into an optimal control problem of the nominal system by properly modifying the cost function to account for all possible uncertainties. Then based on ADP, an adaptive optimal learning algorithm is proposed for the nominal system by using a single critic network with concurrent learning to approximate the solution of Hamilton–Jacobi–Bellman equation. To relax the demands of the persistence of excitation condition, the recorded past data are used simultaneously with the current data for the adaptation of the critic network weights. Besides, an additional adjusting term is employed to stabilise the system and relax the requirement for an initial stabilising control. Moreover, uniform ultimate boundedness of the closed-loop system is guaranteed by using the Lyapunov approach. Finally, three simulation examples are provided to demonstrate the effectiveness of the proposed approach.

An LMI approach to robust optimal guaranteed cost control of 2-D discrete systems described by the Roesser model

The optimal guaranteed cost control problem via static-state feedback controller is addressed in this paper for a class of two-dimensional (2-D) discrete systems described by the Roesser model with norm-bounded uncertainties and a given quadratic cost function. A novel linear matrix inequality (LMI) based criterion for the existence of guaranteed cost controller is established. Furthermore, a convex optimization problem with LMI constraints is formulated to select the optimal guaranteed cost controller which minimizes the guaranteed cost of the closed-loop uncertain system.

Optimal guaranteed cost control of linear uncertain systems: LMI approach

Abstract In this paper, we study the guaranteed cost control problem for a class of linear systems with norm-bounded time-varying parameter uncertainty and a quadratic cost function in a linear matrix inequality (LMI) framework. The solvability condition is expressed as a system of LMIs. Efficient convex optimization techniques are available to solve this system. Moreover, its solutions parametrize the set of guaranteed cost controllers. The LMI-based characterization of guaranteed cost controllers enables us to easily solve the guaranteed cost control problem with some additional requirements. As a result we directly handle the optimal guaranteed cost control problem.