Adaptive optimal backstepping control for strict-feedback nonlinear systems with time-varying partial output constraints

In this work, considering the influence of input saturation and time-varying output constraints, an adaptive neural networks force/position control method is proposed for a class of uncertain robotic manipulators in contact with the external environment. Radial basis function neural networks are introduced to approximate the system uncertainty and only one parameter needs to be updated online. The output constraints are satisfied by converting the constrained system to an unconstrained one. Moreover, an auxiliary dynamic system is applied in the transformed unconstrained system to handle the input saturation nonlinearity and the Moore–Penrose pseudo-inverse term is introduced for controller design. All signals in the closed-loop system are proved to be bounded by using the Lyapunov method. To show the good performance of the given scheme, comparative simulation is conducted on a two-joint manipulator, which is controlled by the proposed adaptive neural networks force/position tracking controller and a conventional force/position controller without considering input saturation and output constraints. Simulation results show that the adaptive neural network force/position controller has better control performance than the traditional method.

Adaptive fuzzy fault-tolerant control problem for a class of uncertain switched stochastic nonlinear systems with time-varying asymmetric output constraints is addressed in this study. Under the action of well-designed asymmetric nonlinear mapping, fuzzy control technology, and backstepping recursive design scheme; the actuator faults of both loss of effectiveness and lock-in-place are considered to develop the adaptive fuzzy controller. The boundedness of all signals as well as the convergence of the output tracking error of the closed-loop plant to an arbitrary small neighborhood about zero are guaranteed by the developed fuzzy adaptive control strategy, and the time-varying output constraints are not violated. A simulation example is worked out to demonstrate the validity of the proposed control scheme.

This article addresses the adaptive tracking control problem of tethered aircraft systems subject to airflow disturbances, output constraints and actuator nonlinearities of saturation, dead-zone, and fault. By combining the nonlinear reconstruction model of the actuator, composed of the ideal and actual reconstruction forms, with the auxiliary system containing a saturation function, the controller design difficulty incurred by actuator nonlinearities is solved. Meanwhile, to guarantee the normal operation of the system under input saturation and output constraints with excessively large initial output values, the constraint function and the auxiliary system building the bridge between input saturation and output constraints are simultaneously introduced to modify the output constraint boundary. Furthermore, considering airflow disturbances, uncertainties and actuator faults in systems, extended state observers are designed to estimate the lumped disturbance. Then, an adaptive tracking controller is proposed to guarantee the outputs meet the modified constraints, and all signals in the closed-loop system are bounded. Finally, the simulation results demonstrate the effectiveness of the proposed controller.

Adaptive neural optimal tracking control of stochastic nonstrict-feedback nonlinear systems with output constraints

Adaptive fuzzy dynamic surface control of nonlinear systems with input saturation and time-varying output constraints

In this paper, a fixed-time backstepping control method is proposed for a six-degree-of-freedom (6-DOF) robot arm system with external disturbances and time-varying symmetric output constraints. Firstly, the fixed-time disturbance observers are designed to accurately and quickly estimate the external disturbances of the robot arm system. Secondly, the fixed-time controller is proposed by combining the backstepping method with the barrier Lyapunov function, to address the output constraint problem of the robot arm system. Simultaneously, a command filter is designed to tackle the “differential explosion” issue in the controller derivation, thus simplifying the control structure of the system and reducing the computational burden of the controller. Theoretical analysis shows that the tracking error of the system can converge to a small neighborhood close to zero within a fixed time, and always meet the requirements of output constraints. Finally, the effectiveness of the proposed method is verified through simulation experiments based on the PUMA560 robot arm system.

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 article, an observer-based fuzzy adaptive inverse optimal output feedback control problem is studied for a class of nonlinear systems in strict-feedback form. The considered nonlinear systems contain unknown nonlinear dynamics and their states are not measured directly. Fuzzy logic systems are applied to identify the unknown nonlinear dynamics and an auxiliary nonlinear system is constructed. Based on this auxiliary system, a fuzzy state observer is first designed to estimate the immeasurable states. By using the inverse optimal principle and adaptive backstepping design theory, an observer-based fuzzy adaptive inverse optimal output feedback control scheme is then developed. The proposed inverse optimal control scheme need not assume that the states are measurable. It also guarantees that the closed-loop system is semiglobally uniformly ultimately bounded, and achieves the optimal control objective as well. Finally, two simulation examples are provided to check the validity of the presented control method.

Water Distribution Networks (WDNs) are crucial for meeting current and future urban water demands. Knowledge of future water demand at different time scales is fundamental for optimal WDN design and operations. Various predictive models of water demand have been proposed in the literature, ranging from traditional time series analysis to cutting-edge machine learning and deep learning techniques. However, the task of forecasting urban water demand remains mostly decoupled from the design of the optimal control of the related WDN. Current performance assessment of demand predictive models focuses predominantly on forecast accuracy, overlooking their practical implications on WDN operations. Meanwhile, the existing research on WDN management often assumes either perfect knowledge of future water demands or employs empirical approximations and aggregate statistics to estimate future water needs. This study bridges this gap by scrutinizing the actual operational value of water demand forecasts in designing optimal operations of WDNs.Here, we develop a forecast-informed optimal WDN control framework to evaluate the operational value of water demand forecasts for WDN operations. Our framework comprises two main modules. The first module computes water demand forecasts. We comparatively evaluate a suite of different forecasting models —including Seasonal Auto-Regressive Integrated Moving Average with eXogenous factors, Multilayer Perceptron, Convolutional Neural Network, and Long Short-Term Memory (a network augmented with an attention mechanism) —across various forecast horizons (1/6/12 hours and 1/3/7/14 days ahead). The most accurate forecasts are integrated into the second module, an economic nonlinear Model Predictive Control (MPC) algorithm designed to optimize WDN operations. Within this module, an Artificial Neural Network (ANN) – based surrogate model encapsulates the hydraulics of the physical WDN, enhancing the optimization process while reducing complexity.We demonstrate our forecast-informed optimal WDN control framework on a real WDN of a rural town with approximately 10,000 inhabitants. Water demand data collected in the Netherlands for a period of 10 years (2007-2017) at 5-minute resolution and corresponding meteorological data are used to train the water demand forecasting models. The MPC module computes the optimal control sequence for 7 pumps and 1 valve in the WDN to minimize pump energy costs while meeting water demands and ensuring safety storage in 5 tanks. Initial findings reveal that the ANN-based surrogate model can accurately incorporate the WDN characteristics (R2 > 0.85), facilitating its integration into the MPC for an efficient and simplified representation of a real-world WDN. Further, MPC fed by 24-hour ahead water demand forecasts achieves potential energy savings of approximately 18% compared to a benchmark rule-based control strategy. Our framework yields a versatile simulation-based optimization tool for evaluating the impact of demand forecasts on WDN management. Future research efforts will aim at refining and comparing deterministic and stochastic water demand forecasts within the MPC framework, under diverse operational objectives.

In this paper, we study the optimal control problem for Takagi–Sugeno (T-S) fuzzy systems with disturbances. Due to the presence of disturbances in the T-S fuzzy systems, a fuzzy optimal state feedback control approach is presented by employing a two-player zero-sum game. Since the analytical optimal control solutions and the worst-case disturbance policies of T-S fuzzy systems can be boiled down to solving the algebraic Riccati equations (AREs), which are difficult to be obtained directly, a model-free policy iteration (PI) learning algorithm is proposed to obtain their approximation solutions. It is proved that the developed fuzzy optimal state feedback controller can ensure the fuzzy systems to be asymptotically stable and satisfy the disturbance attenuation condition simultaneously. Also, the designed PI learning algorithm can converge to their optimal solutions. Finally, we apply the developed fuzzy optimal state feedback control method to the truck-trailer system and the simulation results demonstrated the effectiveness of the developed scheme.

1 A Survey on Computational Optimal Control.- Issues in the Direct Transcription of Optimal Control Problems to Sparse Nonlinear Programs.- Optimization in Control of Robots.- Large-scale SQP Methods and their Application in Trajectory Optimization.- Solving Optimal Control and Pursuit-Evasion Game Problems of High Complexity.- 2 Theoretical Aspects of Optimal Control and Nonlinear Programming.- Continuation Methods In Boundary Value Problems.- Second Order Optimality Conditions for Singular Extremals.- Synthesis of Adaptive Optimal Controls for Linear Dynamic Systems.- Control Applications of Reduced SQP Methods.- Time Optimal Control of Mechanical Systems.- 3 Algorithms for Optimal Control Calculations.- Second Order Algorithm for Time Optimal Control of a Linear System.- An SQP-type Solution Method for Constrained Discrete-Time Optimal Control Problems.- Numerical Methods for Solving Differential Games, Prospective Applications to Technical Problems.- Construction of the Optimal Feedback Controller for Constrained Optimal Control Problems with Unknown Disturbances.- Repetitive Optimization for Predictive Control of Dynamic Systems under Uncertainty.- Optimal Control of Multistage Systems Described by High-Index Differential-Algebraic Equations.- A New Class of a High Order Interior Point Method for the Solution of Convex Semiinfinite Optimization Problems.- A Structured Interior Point SQP Method for Nonlinear Optimal Control Problems.- 4 Software for Optimal Control Calculations.- Automated Approach for Optimizing Dynamic Systems.- ANDECS: A Computation Environment for Control Applications of Optimization.- Application of Automatic Differentiation to Optimal Control Problems.- OCCAL: A mixed symbolic-numeric Optimal Control CALculator.- 5 Applications of Optimal Control.- A Robotic Satellite with Simplified Design.- Nonlinear Control under Constraints of a Biological System.- An Object-Oriented Approach to Optimally Describe and Specify a SCADA System Applied to a Power Network.- Near-Optimal Flight Trajectories Generated by Neural Networks.- Performance of a Feedback Method with Respect to Changes in the Air-Density during the Ascent of a Two-Stage-To-Orbit Vehicle.- Linear Optimal Control for Reentry Flight.- Steady-State Modelling of Turbine Engine with Controllers.- Shortest Paths for Satellite Mounted Robot Manipulators.- Optimal Control of the Industrial Robot Manutec r3.

This paper studies the decentralized optimal control of discrete-time system with inputdelay, where a large number of agents with the identical decoupling dynamical equations and the coupling cost function through the mean field are considered. The decentralized and centralized optimal controllers are proposed by the optimal tracking control of LQR problem with delay. They are proved that the optimal controllers and the optimal cost function of the centralized and decentralized solutions are equivalent for the optimal control problem. An illustrative example is given to show the efficiency of the decentralized optimal controllers.

In this study, a finite‐time online optimal controller was designed for a nonlinear wheeled mobile robotic system (WMRS) with inequality constraints, based on reinforcement learning (RL) neural networks. In addition, an extended cost function, obtained by introducing a penalty function to the original long‐time cost function, was proposed to deal with the optimal control problem of the system with inequality constraints. A novel Hamilton‐Jacobi‐Bellman (HJB) equation containing the constraint conditions was defined to determine the optimal control input. Furthermore, two neural networks (NNs), a critic and an actor NN, were established to approximate the extended cost function and the optimal control input, respectively. The adaptation laws of the critic and actor NN were obtained with the gradient descent method. The semi‐global practical finite‐time stability (SGPFS) was proved using Lyapunov's stability theory. The tracking error converges to a small region near zero within the constraints in a finite period. Finally, the effectiveness of the proposed optimal controller was verified by a simulation based on a practical wheeled mobile robot model.

In this paper, an iterative adaptive dynamic programming (ADP) algorithm is developed to solve the optimal cooperative control problems for residential multi-battery systems. To avoid solving high-dimensional optimal control problems, we first constrain all the batteries at their worst performance, which transforms the multi-input optimal control problem into a single-input one. Based on the worst-performance optimal control law, the optimal cooperative control law for the residential multi-battery systems is obtained, where in each iteration, only a single-input optimization problem is implemented. Finally, numerical results are given to illustrate the performance of the developed algorithm.

Robust [formula omitted] optimal safety control for WMR system with disturbances and actuator attack under event conditions