Optimal Tracking Servo-System by Means of Sliding Mode Control

The conventional optimal tracking control method cannot realize decoupling control of linear systems with a strong coupling property. To solve this problem, in this paper, an optimal decoupling control method is proposed, which can simultaneously provide optimal performance. The optimal decoupling controller is composed of an inner-loop decoupling controller and an outer-loop optimal tracking controller. First, by introducing one virtual control variable, the original differential equation on state is converted to a generalized system on output. Then, by introducing the other virtual control variable, and viewing the coupling terms as the measurable disturbances, the generalized system is open-loop decoupled. Finally, for the decoupled system, the optimal tracking control method is used. It is proved that the decoupling control is optimal for a certain performance index. Simulations on a ball mill coal-pulverizing system are conducted. The results show the effectiveness and superiority of the proposed method as compared with the conventional optimal quadratic tracking &#x0028 LQT &#x0029 control method.

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

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 paper presents an optimal trajectory tracking control algorithm for autonomous surface vessels (ASVs) using data-driven reinforcement learning (RL) to address challenges arising from model uncertainties and time-varying external disturbances in complex marine environments. To ensure robust performance under these conditions, we first employ the H ∞ control method. Then, we design a model-based RL algorithm to achieve the optimal trajectory tracking control law for the ASV despite uncertainties and disturbances. In addition, we extend the model-based RL algorithm to a model-free data-driven RL algorithm, removing the requirement for model of the ASV. The model-free algorithm directly learns the optimal control law from real-time data, providing a more flexible solution when the model of the ASV is unknown. Simulations are conducted to verify the proposed algorithms.

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.

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

In this paper, we study optimal LQG tracking control problems for linear continuous-time hybrid systems. We adopt an approach to prepare some candidates of mode distributions and minimize value functions at each time for the systems and performance indices. By the approach, system states and mode distributions are simultaneously optimized so that the performance indices are minimized for available information of reference signals. We consider optimization problems for averaged systems and averaged performance indices throughout mode distributions. Finally we give numerical examples and verify that we can obtain both optimal tracking performance and optimal candidate of mode distributions by the algorithm presented in this paper.

In this paper, the nonlinear optimal control problem is investigated for spacecraft formation flying with collision avoidance. Based on a nonlinear model of formation flying, two optimal tracking control laws are proposed to ensure the formation pattern converges to the predetermined configuration. The first optimal control law which combines Lyapunov optimizing control with a trajectory-following optimization technique is developed to solve the finite-time nonlinear optimal control problem. For the second controller, an extended [Formula: see text]-[Formula: see text] method is applied to design a closed-form feedback control scheme for nonlinear control problem of spacecraft formation flying with non-standard cost functions. By taking into account the flying safety, a repulsive control scheme is incorporated in the optimal controller to ensure collision avoidance and minimize the performance index. Finally, a numerical example is performed to demonstrate the effectiveness of the proposed approaches.

The paper presents a reinforcement learning approach for optimal tracking control of switched systems with application to a grid-tied hybrid generation system. To enhance interaction with the irregular environment, reference trajectory is learned via controller from states to optimal control. The main issue is to solve the optimal tracking control problem for a hybrid generation system consisting of multiple switched subsystems, and reinforcement learning can seek the globally optimal solution well without knowing accurate system dynamics. The investigated learning algorithm is used to generate an optimum map based on the learned ultimate value without knowledge of system parameters and obtains the optimal control law via deriving of algebraic Riccati equation (ARE) with unnecessary knowing of command generator dynamics. The optimal control solution can converge the online learning algorithm well based on policy iteration as verification in the simulation.

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.

Optimal performance is extremely important for hypersonic flight control. Different from most existing methodologies, which only consider basic control performance including stability, robustness, and transient performance, this article deals with the design of nearly optimal tracking controllers for hypersonic flight vehicles (HFVs). First, main controllers are developed for the velocity subsystem and the altitude subsystem of HFVs via concise fuzzy approximations. Then, optimal controllers are nearly implemented utilizing single-network adaptive critic design. Moreover, the stability of closed-loop systems and the convergence of optimal controllers are theoretically proved. Finally, compared simulation results are given to verify the superiority. The special contribution is the application of a low-complex control structure owing to the critic-only network and advanced learning laws developed for fuzzy approximations, which is expected to guarantee satisfied real-time performance.

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.

The problem of resilient optimal bipartite tracking control for heterogeneous multi-agent systems with multiple targets under denial-of-service (DoS) attacks is investigated in this paper. A bipartite tracking mechanism is devised in which the agents track the targets under bipartite consensus control, which becomes non-autonomous. This is owing to DoS attacks, as the agents cannot obtain real-time information on the tracked targets and neighboring agents. Consequently, A target observer with a storage module has been developed for the efficient estimation of agent states and the storage of observed information as historical data. By recalling the historical data of the observed state, a new type of distributed resilient optimal controller is formulated, which can achieve the control objective in the case of communication blockage, while minimizing the performance index function of the system. Numerical simulations are performed to verify the proposed secure control design.

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.