Trajectory Tracking with Obstacle Avoidance for Nonholonomic Mobile Robots with Diamond-Shaped Velocity Constraints and Output Performance Specifications.

In this paper, we address the trajectory-/target-tracking and obstacle-avoidance problem for nonholonomic mobile robots subjected to diamond-shaped velocity constraints and predefined output performance specifications. The proposed scheme leverages the adaptive performance control to dynamically adjust the user-defined output performance specifications, ensuring compliance with input and safety constraints. A key feature of this approach is the integration of multiple constraints into a single adaptive performance function, governed by a simple adaptive law. Additionally, we introduce a robust velocity estimator with a priori-determined performance attributes to reconstruct the unmeasured trajectory/target velocity. Finally, we validate the effectiveness and robustness of the proposed control scheme, through extensive simulations and a real-world experiment.

Advanced optimal tracking integrating a neural critic technique for asymmetric constrained zero-sum games.

This paper investigates the optimal tracking issue for continuous-time (CT) nonlinear asymmetric constrained zero-sum games (ZSGs) by exploiting the neural critic technique. Initially, an improved algorithm is constructed to tackle the tracking control problem of nonlinear CT multiplayer ZSGs. Also, we give a novel nonquadratic function to settle the asymmetric constraints. One thing worth noting is that the method used in this paper to solve asymmetric constraints eliminates the strict restriction on the control matrix compared to the previous ones. Further, the optimal controls, the worst disturbances, and the tracking Hamilton-Jacobi-Isaacs equation are derived. Next, a single critic neural network is built to estimate the optimal cost function, thus obtaining the approximations of the optimal controls and the worst disturbances. The critic network weight is updated by the normalized steepest descent algorithm. Additionally, based on the Lyapunov method, the stability of the tracking error and the weight estimation error of the critic network is analyzed. In the end, two examples are offered to validate the theoretical results.

Reinforcement Learning-Based Decentralized Safety Control for Constrained Interconnected Nonlinear Safety-Critical Systems.

This paper addresses the problem of decentralized safety control (DSC) of constrained interconnected nonlinear safety-critical systems under reinforcement learning strategies, where asymmetric input constraints and security constraints are considered. To begin with, improved performance functions associated with the actuator estimates for each auxiliary subsystem are constructed. Then, the decentralized control problem with security constraints and asymmetric input constraints is transformed into an equivalent decentralized control problem with asymmetric input constraints using the barrier function. This approach ensures that safety-critical systems operate and learn optimal DSC policies within their safe global domains. Then, the optimal control strategy is shown to ensure that the entire system is uniformly ultimately bounded (UUB). In addition, all signals in the closed-loop auxiliary subsystem, based on Lyapunov theory, are uniformly ultimately bounded, and the effectiveness of the designed method is verified by practical simulation.

Critic Learning-Based Safe Optimal Control for Nonlinear Systems with Asymmetric Input Constraints and Unmatched Disturbances.

In this paper, the safe optimal control method for continuous-time (CT) nonlinear safety-critical systems with asymmetric input constraints and unmatched disturbances based on the adaptive dynamic programming (ADP) is investigated. Initially, a new non-quadratic form function is implemented to effectively handle the asymmetric input constraints. Subsequently, the safe optimal control problem is transformed into a two-player zero-sum game (ZSG) problem to suppress the influence of unmatched disturbances, and a new Hamilton-Jacobi-Isaacs (HJI) equation is introduced by integrating the control barrier function (CBF) with the cost function to penalize unsafe behavior. Moreover, a damping factor is embedded in the CBF to balance safety and optimality. To obtain a safe optimal controller, only one critic neural network (CNN) is utilized to tackle the complex HJI equation, leading to a decreased computational load in contrast to the utilization of the conventional actor-critic network. Then, the system state and the parameters of the CNN are uniformly ultimately bounded (UUB) through the application of the Lyapunov stability method. Lastly, two examples are presented to confirm the efficacy of the presented approach.

Event-triggered adaptive dynamic programming for decentralized tracking control of input constrained unknown nonlinear interconnected systems.

This paper addresses decentralized tracking control (DTC) problems for input constrained unknown nonlinear interconnected systems via event-triggered adaptive dynamic programming. To reconstruct the system dynamics, a neural-network-based local observer is established by using local input-output data and the desired trajectories of all other subsystems. By employing a nonquadratic value function, the DTC problem of the input constrained nonlinear interconnected system is transformed into an optimal control problem. By using the observer-critic architecture, the DTC policy is obtained by solving the local Hamilton-Jacobi-Bellman equation through the local critic neural network, whose weights are tuned by the experience replay technique to relax the persistence of excitation condition. Under the event-triggering mechanism, the DTC policy is updated at the event-triggering instants only. Then, the computational resource and the communication bandwidth are saved. The stability of the closed-loop system is guaranteed by implementing event-triggered DTC policy via Lyapunov's direct method. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed scheme.

Model Predictive Control of a Semi-Active Vehicle-Mounted Vibration Isolation Platform.

When conventional delivery vehicles are driven over complex terrain, large vibrations can seriously affect vehicle-loaded equipment and cargo. Semi-active vehicle-mounted vibration isolation control based on road preview can improve the stability of loaded cargo and instruments by enabling them to have lower vertical acceleration. A combined dynamic model including a vehicle and platform is developed first. In order to obtain a non-linear relationship between damping force and input current, a continuous damping control damper model is developed, and the corresponding external characteristic tests are carried out. Because some conventional control algorithms cannot handle complex constraints and preview information, a model predictive control algorithm based on forward road preview and input constraints is designed. Finally, simulations and real tests of the whole vehicle vibration environment are carried out. The results show that the proposed model predictive control based on road preview can effectively improve vibration isolation performance of the vehicle-mounted platform.

An observer-based adaptive fault-tolerant control for hypersonic vehicle with unexpected centroid shift and input saturation.

This paper makes an investigation on the fault-tolerant control (FTC) problem for a hypersonic reentry vehicle (HSV) in the coexistence of unknown movement of center-of-mass, system input constraint and failure of actuator. Firstly, the dynamics of HSV's attitude system with the unknown factors mentioned above are developed to illustrate the particularity of the researched topic. The influences of unexpected centroid shift on an FTC design can be summarized into the following three parts: unknown system uncertainties, eccentric torque as well as changing system moment of inertia matrix, which are coupled and unknown. Secondly, due to the difficulty in decoupling and estimating these influences (embodied in the output states of the system) one by one, it is the attitude system states observer that is proposed to estimate those detrimental unknown effects. The designed observer is consisted of an adaptive fault observer and an adaptive sliding-mode observer, supporting an innovative adaptive FTC scheme free from the variation of inverse matrix that might be singular due to an unexpected centroid shift. This fault-tolerant controller established in the estimated system states is derived by utilizing the above mentioned observer and adaptive backstepping control in conjunction with adaptive auxiliary compensation systems to handle the system input saturation. Moreover, the convergence of attitude tracking error and the boundedness of all closed-loop signals are achieved in the light of Lyapunov stability theory and boundedness analysis. Ultimately, simulation results are delivered to demonstrate the effectiveness of the proposed FTC scheme.

Steady-state sequence optimization with incremental input constraints in two-layer model predictive control.

Steady-state optimization is of vital importance in two-layer model predictive control for bringing better steady-state and dynamic performance. However, the global optimality of steady-state sequences provided by local steady-state optimization cannot be guaranteed. Therefore, a new steady-state sequence optimization approach is proposed in the paper, to improve the global optimality of steady-state sequences. First, the non-global optimality of local steady-state sequences is discussed using an example. Subsequently, aiming at improving the global optimality, a novel sequence optimization strategy designed for steady-state optimization is proposed. Its basic formulation is given and the lower bound of the introduced parameter is analyzed. Then, the relation and difference between the proposed steady-state sequence optimization and the existing global steady-state optimization and local steady-state optimization are discussed. Finally, the steady-state performance, dynamic performance, and computational burden of the proposed approach are studied. The proposed approach provides engineers a brand-new way to realize steady-state optimization and effectively improves the global optimality of calculated steady-state sequences. Extensive simulations verify the effectiveness and reliability of the proposed method.

Observer-based event-triggered control for zero-sum games of input constrained multi-player nonlinear systems.

In this paper, an event-triggered control (ETC) method is investigated to solve zero-sum game (ZSG) problems of unknown multi-player continuous-time nonlinear systems with input constraints by using adaptive dynamic programming (ADP). To relax the requirement of system dynamics, a neural network (NN) observer is constructed to identify the dynamics of multi-player system via the input and output data. Then, the event-triggered Hamilton-Jacobi-Isaacs (HJI) equation of the ZSG can be solved by constructing a critic NN, and the approximated optimal control law and the worst disturbance law can be obtained directly. A triggering scheme which determines the updating time instants of the control law and the disturbance law is developed. Thus, the proposed ADP-based ETC method cannot only reduce the computational burden, but also save communication resource and bandwidths. Furthermore, we prove that the signals of the closed-loop system and the approximate errors of the critic NN weights are uniformly ultimately bounded by using Lyapunov's direct method, and the Zeno behavior is excluded. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed ETC scheme.

A Robust Fault-Tolerant Predictive Control for Discrete-Time Linear Systems Subject to Sensor and Actuator Faults.

In this paper, a robust fault-tolerant model predictive control (RFTPC) approach is proposed for discrete-time linear systems subject to sensor and actuator faults, disturbances, and input constraints. In this approach, a virtual observer is first considered to improve the observation accuracy as well as reduce fault effects on the system. Then, a real observer is established based on the proposed virtual observer, since the performance of virtual observers is limited due to the presence of unmeasurable information in the system. Based on the estimated information obtained by the observers, a robust fault-tolerant model predictive control is synthesized and used to control discrete-time systems subject to sensor and actuator faults, disturbances, and input constraints. Additionally, an optimized cost function is employed in the RFTPC design to guarantee robust stability as well as the rejection of bounded disturbances for the discrete-time system with sensor and actuator faults. Furthermore, a linear matrix inequality (LMI) approach is used to propose sufficient stability conditions that ensure and guarantee the robust stability of the whole closed-loop system composed of the states and the estimation error of the system dynamics. As a result, the entire control problem is formulated as an LMI problem, and the gains of both observer and robust fault-tolerant model predictive controller are obtained by solving the linear matrix inequalities (LMIs). Finally, the efficiency of the proposed RFTPC controller is tested by simulating a numerical example where the simulation results demonstrate the applicability of the proposed method in dealing with linear systems subject to faults in both actuators and sensors.

Neural network-based model predictive tracking control of an uncertain robotic manipulator with input constraints.

This paper proposes a neural network-based model predictive control (MPC) method for robotic manipulators with model uncertainty and input constraints. In the presented NN-based MPC structure, two groups of radial basis function neural networks (RBFNNs) are considered for online model estimation and effective optimization. The first group of RBFNNs is introduced as a predictive model for the robotic system with online learning strategies for handling the system uncertainty and improving the model estimation accuracy. The second one is developed for solving the optimization problem. By taking into account an actor-critic scheme with different weights and the same activation function, adaptive learning strategies are established for balancing between optimal tracking performance and predictive system stability. In addition, aiming at guaranteeing the input constraints, a nonquadratic cost function is adopted for the NN-based MPC. The ultimately uniformly boundedness (UUB) of all variables is verified through the Lyapunov approach. Simulation studies are conducted to explain the effectiveness of the proposed method.

Observer-based control for nonlinear parameter-varying systems: A sum-of-squares approach.

This paper investigates the design problem of nonlinear and time-varying observer-based controllers for nonlinear parameter-varying systems without/with input constraints. With the aid of Lyapunov stability theory, the state-and-parameter-dependent linear matrix inequality conditions are obtained. These conditions are developed as convex programming problems. And a feasible solution can be obtained via sum-of-squares techniques. Thus, the commonly used backstepping/iterative methods are avoided. In addition, the effect of the bilinear product forms for the controller gain matrix and the Lyapunov functional are eliminated. A remarkable advantage of this proposed approach is that the state-and-parameter-dependent observer and the state-feedback controller can be designed independently, which significantly reduces the computational complexity. Finally, the feasibility and validity of the proposed method can be illustrated by simulation results.

Auxiliary-system-based composite adaptive optimal backstepping control for uncertain nonlinear guidance systems with input constraints.

This paper addresses a missile-target interception guidance process considering acceleration saturation and target maneuver as a constrained nonlinear tracking issue. A dynamic auxiliary system is designed for compensating the effects of constrained input, and external disturbances are counteracted through designing a nonlinear disturbance observer (NDO). The feedforward+feedback composite architecture is built in which a feedforward backstepping control and a feedback optimal control is presented recurrently. Furthermore, the parameter adaptive updating laws are derived to estimate the unknown functions online. Subsequently, the boundedness of the closed-loop signals are guaranteed. The predefined cost function is also ensured to be minimized. Furthermore, the control input is prevented violating its boundary. The contrastive simulation results demonstrate that the robustness of the proposed method is more superior to the nonsingular terminal sliding mode (NTSM) and the proportional navigation (PN) methods.

Fuzzy-approximation-based prescribed performance control of air-breathing hypersonic vehicles with input constraints.

In this article, aiming at the longitudinal dynamics model of air-breathing hypersonic vehicles, a fuzzy-approximation-based prescribed performance control scheme with input constraints is proposed. First, this article presents a novel prescribed performance function, which does not depend on the sign of initial tracking error. And combining prescribed performance control method with backstepping control, the control scheme can ensure that system can converge at a prescribed rate of convergence, overshoot, and steady-state error. In order to solve the problem that backstepping control method needs to be differentiated multiple times, fuzzy approximators are used to estimate the unknown functions, and norm estimation approach is used to simplify the computation of fuzzy approximator. Aiming at the problem of input saturation of actuator in subsystem of air-breathing hypersonic vehicle, the new auxiliary system is designed to ensure the stability and robustness of air-breathing hypersonic vehicle system under input constraints. Finally, the effectiveness of the proposed control strategy is verified by simulation analysis.

Modeling and sliding mode predictive control of the ultra-supercritical boiler-turbine system with uncertainties and input constraints.

The coordinated control system (CCS) serves as an important role in load regulation, efficiency optimization and pollutant reduction for coal-fired power plants. The CCS faces with tough challenges, such as the wide-range load variation, various uncertainties and constraints. This paper aims to improve the load tacking ability and robustness for boiler-turbine units under wide-range operation. To capture the key dynamics of the ultra-supercritical boiler-turbine system, a nonlinear control-oriented model is developed based on mechanism analysis and model reduction techniques, which is validated with the history operation data of a real 1000 MW unit. To simultaneously address the issues of uncertainties and input constraints, a discrete-time sliding mode predictive controller (SMPC) is designed with the dual-mode control law. Moreover, the input-to-state stability and robustness of the closed-loop system are proved. Simulation results are presented to illustrate the effectiveness of the proposed control scheme, which achieves good tracking performance, disturbance rejection ability and compatibility to input constraints.

Health care input constraints and cost effectiveness analysis decision rules.

Results of cost effectiveness analyses (CEA) studies are most useful for decision makers if they face only one constraint: the health care budget. However, in practice, decision makers wishing to use the results of CEA studies may face multiple resource constraints relating to, for instance, constraints in health care inputs such as a shortage of skilled labour. The presence of multiple resource constraints influences the decision rules of CEA and limits the usefulness of traditional CEA studies for decision makers. The goal of this paper is to illustrate how results of CEA can be interpreted and used in case a decision maker faces a health care input constraint. We set up a theoretical model describing the optimal allocation of the health care budget in the presence of a health care input constraint. Insights derived from that model were used to analyse a stylized example based on a decision about a surgical robot as well as a published cost effectiveness study on eye care services in Zambia. Our theoretical model shows that applying default decision rules in the presence of a health care input constraint leads to suboptimal decisions but that there are ways of preserving the traditional decision rules of CEA by reweighing different cost categories. The examples illustrate how such adjustments can be made, and makes clear that optimal decisions depend crucially on such adjustments. We conclude that it is possible to use the results of cost effectiveness studies in the presence of health care input constraints if results are properly adjusted.

A policy iteration approach to online optimal control of continuous-time constrained-input systems.

This paper is an effort towards developing an online learning algorithm to find the optimal control solution for continuous-time (CT) systems subject to input constraints. The proposed method is based on the policy iteration (PI) technique which has recently evolved as a major technique for solving optimal control problems. Although a number of online PI algorithms have been developed for CT systems, none of them take into account the input constraints caused by actuator saturation. In practice, however, ignoring these constraints leads to performance degradation or even system instability. In this paper, to deal with the input constraints, a suitable nonquadratic functional is employed to encode the constraints into the optimization formulation. Then, the proposed PI algorithm is implemented on an actor-critic structure to solve the Hamilton-Jacobi-Bellman (HJB) equation associated with this nonquadratic cost functional in an online fashion. That is, two coupled neural network (NN) approximators, namely an actor and a critic are tuned online and simultaneously for approximating the associated HJB solution and computing the optimal control policy. The critic is used to evaluate the cost associated with the current policy, while the actor is used to find an improved policy based on information provided by the critic. Convergence to a close approximation of the HJB solution as well as stability of the proposed feedback control law are shown. Simulation results of the proposed method on a nonlinear CT system illustrate the effectiveness of the proposed approach.