Distributed H∞ Optimal Tracking Control for Strict-Feedback Nonlinear Large-Scale Systems With Disturbances and Saturating Actuators

The optimal output tracking control problem for nonlinear large-scale dynamic systems is considered. A series-based approximate approach for designing the optimal controller is proposed with respect to quadratic performance indexes. By using the approach, the high order, coupling, nonlinear two-point boundary value problem is transformed into a sequence of linear decoupling two-point boundary value problems. By intercepting the frontal finite terms of the solution series, we obtained a suboptimal tracking control law. A simulation example illustrates the efficiency of the optimal output tracking control law designed.

This chapter presents an optimal tracking control methodology for an offshore steel jacket platform subject to external wave force. Based on a dynamic model of an offshore steel jacket platform with an AMD mechanism and a linear exogenous system model of the external wave force on the offshore platform, an optimal tracking control scheme with feedforward compensation is proposed to attenuate wave-induced vibration of the offshore platform. A feedforward and feedback optimal tracking controller (FFOTC) can be obtained by solving an algebraic Riccati equation and a Sylvester equation, respectively. It is demonstrated that the wave-induced vibration amplitudes of the offshore platform under the FFOTC are much smaller than the ones under the feedback optimal tracking controller (FOTC) and the feedforward and feedback optimal controller (FFOC). Furthermore, the required control force under the FFOTC is smaller than the ones under the FOTC and the FFOC.

This article addresses the optimal tracking control problem with prescribed performance for uncertain nonlinear systems subject to input constraint and unknown disturbances. First, a fixed‐time monotonic convergence function is introduced to restrain tracking error, and a nonlinear mapping technique is employed to transform the constrained error into an unconstrained variable, then the fixed‐time output tracking issue is boiled down to the boundedness problem of the transformed variable. With the aid of a nonquadratic cost function, the input constraint is encoded into the optimization problem. To solve the unknown disturbances, an auxiliary system and an auxiliary disturbance policy are constructed, and the optimal control problem is formulated as a two‐player zero‐sum game. Moreover, a Hamilton–Jacobi–Isaacs (HJI) equation associated with this nonquadratic zero‐sum game is established to give the optimal control and the worst‐case disturbance policy solution. Subsequently, to avoid using knowledge of the system dynamics, three neural network approximators, namely, actor, critic, and disturbance, which are tuned online and simultaneously for approximating the solution of HJI, are constructed based on the integral reinforcement learning algorithm. Theoretical analysis shows that the reconstructed error system states and the weight estimation errors are semi‐globally uniformly ultimately bounded. Finally, the simulation study further tests the availability of the proposed control strategy.

In this paper an infinite-time optimal tracking control scheme is presented for a class of discrete-time non-affine systems, where the optimal tracking controller is composed of two sub-controllers: the feedforward controller and the feedback controller. The feedforward controller is designed by implicit function theorem, while the feedback controller is realized by the greedy Globalized Dual Heuristic Programming (GDHP) iteration algorithm. To facilitate the implementation of the algorithm, three neural networks are adopted. The simulation results have demonstrated the validity of the proposed optimal tracking control scheme.

This paper studies the problem of optimal parallel tracking control for continuous-time general nonlinear systems. Unlike existing optimal state feedback control, the control input of the optimal parallel control is introduced into the feedback system. However, due to the introduction of control input into the feedback system, the optimal state feedback control methods can not be applied directly. To address this problem, an augmented system and an augmented performance index function are proposed firstly. Thus, the general nonlinear system is transformed into an affine nonlinear system. The difference between the optimal parallel control and the optimal state feedback control is analyzed theoretically. It is proven that the optimal parallel control with the augmented performance index function can be seen as the suboptimal state feedback control with the traditional performance index function. Moreover, an adaptive dynamic programming ( ADP ) technique is utilized to implement the optimal parallel tracking control using a critic neural network ( NN ) to approximate the value function online. The stability analysis of the closed-loop system is performed using the Lyapunov theory, and the tracking error and NN weights errors are uniformly ultimately bounded ( UUB ) . Also, the optimal parallel controller guarantees the continuity of the control input under the circumstance that there are finite jump discontinuities in the reference signals. Finally, the effectiveness of the developed optimal parallel control method is verified in two cases.

With the increasing deployment of Unmanned Aerial Vehicle (UAV) swarms in uncertain and dynamically changing environments, optimal cooperative control has become essential for ensuring robust and efficient system coordination. To this end, this paper designs a data-driven optimal bipartite containment tracking control scheme for multi-UAV systems under compound uncertainties. A novel Dynamic Iteration Regulation Strategy (DIRS) is proposed, which enables real-time adjustment of the learning iteration step according to the task-specific demands. Compared with conventional fixed-step data-driven algorithms, the DIRS provides greater flexibility and computational efficiency, allowing for better trade-offs between the performance and cost. First, the optimal bipartite containment tracking control problem is formulated, and the associated coupled Hamilton–Jacobi–Bellman (HJB) equations are established. Then, a data-driven iterative policy learning algorithm equipped with the DIRS is developed to solve the optimal control law online. The stability and convergence of the proposed control scheme are rigorously analyzed. Furthermore, the control law is approximated via the neural network framework without requiring full knowledge of the model. Finally, numerical simulations are provided to demonstrate the effectiveness and robustness of the proposed DIRS-based optimal containment tracking scheme for multi-UAV systems, which can reduce the number of iterations by 88.27% compared to that for the conventional algorithm.

This paper considers the global optimal control for nonlinear interconnected large-scale systems with respect to linear quadratic functional. A successive approximation procedure is proposed to design the feedforward feedback nearly optimal control law. By introducing the Successive Approximation Approach of the nonlinear differential equation theory, a nonhomogeneous linear two-point boundary value problem sequence is constructed to approximate the nonlinear large-scale two-point boundary value problem, which is the necessary condition of the nonlinear control problem. By iteratively solving this nonhomogeneous linear approximating sequence, a global nearly optimal control law that composed of a linear closed-loop feedback compensatory term and an open-loop feedforward compensatory term is designed. An algorithm is presented to design certain qualified nearly optimal control law by truncating an infinite iteration result. An illustrative example shows the validity of the algorithm.

Data-based adaptive neural network optimal output feedback control for nonlinear systems with actuator saturation

Optimal tracking control with zero steady-state error for time-delay systems with sinusoidal disturbances

Optimal trajectory tracking control of robotic manipulator system added by discrete-time fast terminal sliding mode predictive approach.

For the optimal tracking control problem of affine nonlinear systems, a general value iteration algorithm based on adaptive dynamic programming is proposed in this paper. By system transformation, the optimal tracking problem is converted into the optimal regulating problem for the tracking error dynamics. Then, general value iteration algorithm is developed to obtain the optimal control with convergence analysis. Considering the advantages of echo state network, we use three echo state networks with levenberg-Marquardt (LM) adjusting algorithm to approximate the system, the cost function and the control law. A simulation example is given to demonstrate the effectiveness of the presented scheme.

In this paper, online optimal adaptive tracking control of nonlinear discrete-time systems in affine form with uncertain internal dynamics is presented. The augmented system and the cost function over infinite horizon for the augmented state are defined. Two-layer neural network (NN) -based actor-critic framework is introduced to estimate the optimal control input and value function. The temporal difference (TD) error is derived as a function of the difference between actual and estimated value function. The NN weights of critic and actor are tuned at every sampling instant as a function of the instantaneous temporal difference errors and control policy errors, respectively. The proposed scheme ensures the closed-loop stability in the form of boundedness. Simulation results are provided to illustrate the effectiveness of the proposed approach.

The optimal output tracking control(OOTC) problem is considered for continuous linear time-invariable systems, which include control delays and external sinusoidal disturbances. We first transform the original system into a new system without time-delay, then construct a new state vector, which containing a external system’s vector. The external system described the aim which we want to track. Following the law of internal model principle, we transform the original and external systems into a new augmented system. Finally we get an optimal control law according to the optimal performance index, and prove the method is effective by emulation.

This paper addresses the development of a dynamic programming decomposition-coordination algorithm for the optimal control of discrete-time large-scale systems with multiple time delays. The systems under study can be converted into the corresponding augmented systems satisfying the Markov processes denning the augmented state vectors. The resulting dynamic programming can then be further decomposed into a series of subproblems which might be solved in parallel by combining the dynamic programming techniques with approaches to matrix partition. The entire system's solution is finally given by the iterative computation between the subproblems being the local control level and the coordinator. The major advantages of the proposed algorithm over others are to avoid two-point boundary-value problems of the systems with multiple time delays and to significantly reduce the computer memory and time required for such large-scale systems optimal control problems.

Learning-based optimal cooperative control using edge-based triggering strategy