Output-Feedback Based Simplified Optimized Backstepping Control for Strict-Feedback Systems with Input and State Constraints

In this paper,an adaptive neural-network(NN)output feedback optimal control problem is studied for a class of strict-feedback nonlinear systems with unknown internal dynamics,input saturation and state constraints.Neural networks are used to approximate unknown internal dynamics and an adaptive NN state observer is developed to estimate immeasurable states.Under the framework of the backstepping design,by employing the actor-critic architecture and constructing the tan-type Barrier Lyapunov function(BLF),the virtual and actual optimal controllers are developed.In order to accomplish optimal control effectively,a simplified reinforcement learning(RL)algorithm is designed by deriving the updating laws from the negative gradient of a simple positive function,instead of employing existing optimal control methods.In addition,to ensure that all the signals in the closed-loop system are bounded and the output can follow the reference signal within a bounded error,all state variables are confined within their compact sets all times.Finally,a simulation example is given to illustrate the effectiveness of the proposed control strategy.

SEQUENTIAL QUADRATIC PROGRAMMING METHODS FOR OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS

A kind of direct methods is presented for the solution of optimal control problems with state constraints. These methods are sequential quadratic programming methods. At every iteration a quadratic programming which is obtained by quadratic approximation to Lagrangian function and linear approximations to constraints is solved to get a search direction for a merit function. The merit function is formulated by augmenting the Lagrangian function with a penalty term. A line search is carried out along the search direction to determine a step length such that the merit function is decreased. The methods presented in this paper include continuous sequential quadratic programming methods and discreate sequential quadratic programming methods.

OPTIMAL CONTROL OF HYPERBOLIC H-HEMIVARIATIONAL INEQUALITIES WITH STATE CONSTRAINTS

The optimal control problems of hyperbolic H-hemivariational inequalities with the state constraints and nonnomotone multivalued mapping term are considered.The optimal solutions are obtained.In addition,their approximating problems are also studied.

Adaptive Barrier-Lyapunov-Functions Based Control Scheme of Nonlinear Pure-Feedback Systems with Full State Constraints and Asymptotic Tracking Performance

In this paper,the authors propose an adaptive Barrier-Lyapunov-Functions(BLFs)based control scheme for nonlinear pure-feedback systems with full state constraints.Due to the coexist of the non-affine structure and full state constraints,it is very difficult to construct a desired controller for the considered system.According to the mean value theorem,the authors transform the pure-feedback system into a system with strict-feedback structure,so that the well-known backstepping method can be applied.Then,in the backstepping design process,the BLFs are employed to avoid the violation of the state constraints,and neural networks(NNs)are directly used to online approximate the unknown packaged nonlinear terms.The presented controller ensures that all the signals in the closed-loop system are bounded and the tracking error asymptotically converges to zero.Meanwhile,it is shown that the constraint requirement on the system will not be violated during the operation.Finally,two simulation examples are provided to show the effectiveness of the proposed control scheme.

Asymmetric time-varying integral barrier Lyapunov function based adaptive optimal control for nonlinear systems with dynamic state constraints

This paper investigates the issue of adaptive optimal tracking control for nonlinear systems with dynamic state constraints.An asymmetric time-varying integral barrier Lyapunov function(ATIBLF)based integral reinforcement learning(IRL)control algorithm with an actor–critic structure is first proposed.The ATIBLF items are appropriately arranged in every step of the optimized backstepping control design to ensure that the dynamic full-state constraints are never violated.Thus,optimal virtual/actual control in every backstepping subsystem is decomposed with ATIBLF items and also with an adaptive optimized item.Meanwhile,neural networks are used to approximate the gradient value functions.According to the Lyapunov stability theorem,the boundedness of all signals of the closed-loop system is proved,and the proposed control scheme ensures that the system states are within predefined compact sets.Finally,the effectiveness of the proposed control approach is validated by simulations.

Event-triggered adaptive finite-time control for nonlinear systems under asymmetric time-varying state constraints

This paper investigates the issue of event-triggered adaptive finite-time state-constrained control for multi-input multi-output uncertain nonlinear systems.To prevent asymmetric time-varying state constraints from being violated,a tan-type nonlinear mapping is established to transform the considered system into an equivalent“non-constrained”system.By employing a smooth switch function in the virtual control signals,the singularity in the traditional finite-time dynamic surface control can be avoided.Fuzzy logic systems are used to compensate for the unknown functions.A suitable event-triggering rule is introduced to determine when to transmit the control laws.Through Lyapunov analysis,the closed-loop system is proved to be semi-globally practical finite-time stable,and the state constraints are never violated.Simulations are provided to evaluate the effectiveness of the proposed approach.

Event-Triggered Adaptive Neural Control for Multiagent Systems with Deferred State Constraints

This paper focuses on the leader-following consensus control problem for nonlinear multiagent systems subject to deferred asymmetric time-varying state constraints.A distributed eventtriggered adaptive neural control approach is advanced.By virtue of a distributed sliding-mode estimator,the leader-following consensus control problem is converted into multiple simplified tracking control problems.Afterwards,a shifting function is utilized to transform the error variables such that the initial tracking condition can be totally unknown and the state constraints can be imposed at a specified time instant.Meanwhile,the deferred asymmetric time-varying full state constraints are addressed by a class of asymmetric barrier Lyapunov function.In order to reduce the burden of communication,a relative threshold event-triggered mechanism is incorporated into controller and Zeno behavior is excluded.Based on Lyapunov stability theorem,all closed-loop signals are proved to be semi-globally uniformly ultimately bounded.Finally,a practical simulation example is given to verify the presented control scheme.

Stochastic maximum principle for mean-field forward-backward stochastic control system with terminal state constraints

In this paper,we consider an optimal control problem with state constraints,where the control system is described by a mean-field forward-backward stochastic differential equation(MFFBSDE,for short)and the admissible control is mean-field type.Making full use of the backward stochastic differential equation theory,we transform the original control system into an equivalent backward form,i.e.,the equations in the control system are all backward.In addition,Ekeland's variational principle helps us deal with the state constraints so that we get a stochastic maximum principle which characterizes the necessary condition of the optimal control.We also study a stochastic linear quadratic control problem with state constraints.

Stabilization of linear time-varying systems with state and input constraints using convex optimization

The stabilization problem of linear time-varying systems with both state and input constraints is considered. Sufficient conditions for the existence of the solution to this problem are derived and a gain-switched（gain-scheduled） state feedback control scheme is built to stabilize the constrained timevarying system. The design problem is transformed to a series of convex feasibility problems which can be solved efficiently. A design example is given to illustrate the effect of the proposed algorithm.

Multigrid Methods for Elliptic Optimal Control Problems with Pointwise State Constraints

An elliptic optimal control problem with constraints on the state variable is considered.The Lavrentiev-type regularization is used to treat the constraints on the state variable.To solve the problem numerically,the multigrid for optimization(MGOPT)technique and the collective smoothing multigrid(CSMG)are implemented.Numerical results are reported to illustrate and compare the efficiency of both multigrid strategies.

Adaptive fuzzy asymptotic control design for MIMO nonlinear systems with state constraints

This paper addresses the asymptotic control problem of uncertain multi-input and multi-output(MIMO)nonlinear systems.The considered MIMO systems contain unknown virtual control coefficients(UVCCs)and state constraints.Acreative Lyapunov function by associating with the lower bounds of UVCCs is presented to counteract the adverse effect deriving from UVCCs.The state constraints are ensured by utilising the barrier Lyapunov function.Moreover,the asymptotic tracking controller is recursively constructed by combining the backstepping technique with fuzzy logic systems.The remarkable character of the designed controller is that the asymptotic tracking performance can be achieved by introducing some smooth functions into adaptive backstepping procedure.In contrast to the existing results,the conditions on the UVCCs are relaxed.Finally,the new control design is illustrated by a practical example.

A Maximum Principle for Fully Coupled Forward-Backward Stochastic Control System Driven by Lvy Process with Terminal State Constraints

This paper is concerned with a fully coupled forward-backward stochastic optimal control problem where the controlled system is driven by Levy process, while the forward state is constrained in a convex set at the terminal time. The authors use an equivalent backward formulation to deal with the terminal state constraint, and then obtain a stochastic maximum principle by Ekeland＇s variational principle. Finally, the result is applied to the utility optimization problem in a financial market.

Adaptive Sliding-Mode Disturbance Observer-Based Nonlinear Control for Unmanned Dual-Arm Aerial Manipulator Subject to State Constraints

The unmanned dual-arm aerial manipulator system is composed of a multirotor unmanned aerial vehicle(UAV)and two manipulators.Compared to a single manipulator,dual-arm always provides greater°exibility and versatility in both goods delivery and complex task execution.However,the practical application of the system is limited due to nonlinearities and complex dynamic coupling behavior between the multirotor and the manipulator,as well as the one between the inner and outer loop of the multirotor.In this paper,a holistic model of the dual-arm aerial manipulator system is¯rst derived with complete model information.Subsequently,an adaptive sliding-mode disturbance observer(ASMDO)is proposed to handle external disturbances and unmeasurable disturbances caught by unmeasurable angular velocity and acceleration of the manipulators.Moreover,for safety concerns and transient performance requirements,the state constraints should be guaranteed.To this end,an auxiliary term composed of constrained variable signals is introduced.Then,the performance of the designed method is proven by rigorous analysis.Finally,the proposed method is validated through two sets of simulation tests.

Reduced-order Kalman filtering for state constrained linear systems

This paper aims at solving the state filtering problem for linear systems with state constraints. Three classes of typical state constraints, i.e., linear equality, quadratic equality and inequality, are discussed. By using the linear relationships among different state variables, a reduced-order Kalman filter is derived for the system with linear equality constraints. Afterwards, such a solution is applied to the cases of the quadratic equality constraint and inequality constraints and the two constrained state filtering problems are transformed into two relative constrained optimization problems. Then they are solved by the Lagrangian multiplier and linear matrix inequality techniques, respectively. Finally, two simple tracking examples are provided to illustrate the effectiveness of the reduced-order filters.

NECESSARY CONDITIONS FOR OPTIMAL CONTROLS OF SEMILINEAR ELLIPTIC VARIATIONAL INEQUALITIES INVOLVING STATE CONSTRAINT

This paper deals with maximum principle for some optimal control problem governed by some elliptic variational inequalities. Some state constraints are discussed. The basic techniques used here are based on those in [1] and a new penalty functional defined in this paper.

OPTIMAL CONTROL OF PARABOLIC VARIATIONAL INEQUALITIES WITH STATE CONSTRAINT

The optimal control problem of parabolic variational inequalities with the state constraint and nonlinear, discontinuous nonmonotone multivalued mapping term and its approximating problem are studied, which generalizes some obtained results.

Aero-thermal heating constrained midcourse guidance using state-constrained model predictive static programming method

This paper proposes a multiple-constraints-guaranteed midcourse guidance law for the interception of the hypersonic targets. In traditional midcourse law design, the constraints of the aero-thermal heating are rarely taken into consideration. The performance of the infrared detection system may be degraded and the instability of the flight control system may be induced.To address this problem, a state-constrained model predictive static programming method is introduced such that both terminal constraints(position and angle) and optimal energy consumption can be ensured. As a result, a sub-optimal midcourse guidance,guaranteeing the aforementioned multiple-constraints to be never violated, is synthesized. Simulation results demonstrate the effectiveness of the proposed method.

FINITE ELEMENT ANALYSIS OF OPTIMAL CONTROL PROBLEM GOVERNED BY STOKES EQUATIONS WITH L^2-NORM STATE-CONSTRAINTS

An optimal control problem governed by the Stokes equations with L^2-norra state constraints is studied. Finite element approximation is constructed. The optimality conditions of both the exact and discretized problems are discussed, and the a priori error estimates of the optimal order accuracy in L^2-norm and H^1-norm are given. Some numerical experiments are presented to verify the theoretical results.

VARIATIONAL DISCRETIZATION OF PARABOLIC CONTROL PROBLEMS IN THE PRESENCE OF POINTWISE STATE CONSTRAINTS

space dimensions. These bounds follow from uniform estimates for the discretization error of the state under natural regularity requirements.

WEAK-DUALITY BASED ADAPTIVE FINITE ELEMENT METHODS FOR PDE-CONSTRAINED OPTIMIZATION WITH POINTWISE GRADIENT STATE-CONSTRAINTS

Adaptive finite element methods for optimization problems for second order linear el- liptic partial differential equations subject to pointwise constraints on the l2-norm of the gradient of the state are considered. In a weak duality setting, i.e. without assuming a constraint qualification such as the existence of a Slater point, residual based a posteriori error estimators are derived. To overcome the lack in constraint qualification on the continuous level, the weak Fenchel dual is utilized. Several numerical tests illustrate the performance of the proposed error estimators.Mathematics subject classification： 65N30, 90C46, 65N50, 49K20, 49N15, 65K10.