Online adaptive algorithm for optimal control of structures subjected to travelling loads

Approaching the problem of optimal adaptive control as ldquooptimal control made adaptive,rdquo namely, as a certainty equivalence combination of linear quadratic optimal control and standard parameter estimation, fails on two counts: numerical (as it requires a solution to a Riccati equation at each time step) and conceptual (as the combination actually does not possess any optimality property). In this note, we present a particular form of optimality achievable in Lyapunov-based adaptive control. State and control are subject to positive definite penalties, whereas the parameter estimation error is penalized through an exponential of its square, which means that no attempt is made to enforce the parameter convergence, but the estimation transients are penalized simultaneously with the state and control transients. The form of optimality we reveal here is different from our work in [Z. H. Li and M. Krstic, ldquoOptimal design of adaptive tracking controllers for nonlinear systems,rdquo <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Automatica</i> , vol. 33, pp. 1459-1473, 1997] where only the terminal value of the parameter error was penalized. We present our optimality concept on a partial differential equation (PDE) example-boundary control of a particular parabolic PDE with an unknown reaction coefficient. Two technical ideas are central to the developments in the note: a nonquadratic Lyapunov function and a normalization in the Lyapunov-based update law. The optimal adaptive control problem is fundamentally nonlinear and we explore this aspect through several examples that highlight the interplay between the non-quadratic cost and value functions.

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.

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.

This article focuses on the problem of adaptive optimal tracking control of interconnected switched systems on dwell time. The objective is to establish interconnection between switched systems, stabilize each switched system, and achieve optimal performance over the dwell time. An actor-critic learning technique is utilized to design the optimal controller by evaluating the performance via the critic and improving the policy via the actor. During the design of the cost function and optimization process, we employed non-zero-sum game theory to incorporate the interconnection factors among systems. The proposed control scheme designs a novel relaxed stability condition for switched subsystems and validates the effectiveness by using a Lyapunov function with a value function. Finally, the designed control scheme can be verified by simulation.

Voronoi-based adaptive area optimal coverage control for multiple manipulator systems with uncertain kinematics and dynamics

OPTIMAL ADAPTIVE ROBUST CONTROLLER FOR HYDROTURBINE REGULATION

Optimal Adaptive Robust Controller for Hydroturbine Regulation

This paper investigates the problem of attitude control and disturbance rejection of rigid spacecraft in the presence of parameter uncertainty. The Modified Rodrigues Parameter (MRP) is used along with its associated shadow set as the kinematic variables since it forms a nonsingular set for all possible rotations. The parameter uncertainty caused by the unknown inertia matrix is handled by combining the semitensor product and adaptive control method. Then the synergetic optimal controller (SOC) is designed. This adaptive optimal attitude control algorithm can eliminate inertia parameters' uncertainty and reject disturbance with zero steady-state error and they have optimality property with respect to a meaningful cost functional. Simulation results are employed to confirm the effectiveness of the proposed approach.

The use of an adaptive optimal control algorithm for two real-time control applications, an optimal excitation control of a synchronous generator (OEC) and a power system stabilizer (PSS), is described. Experimental studies on a physical model of a power system showed that the proposed OEC and PSS can track the controlled system by parameter identification at different operating conditions. The proposed algorithm is based on linear optimal control theory. A special fifth-order discrete Riccati equation is solved in each sampling period. The proposed OEC and PSS can always guarantee that in a closed loop the controlled system will be stable based on the identified parameters. As the actual output of the controlled system and control are directly used in the controller, no observer is required. The proposed OEC and PSS can track the controlled system very rapidly. A number of tests have been performed, and all show satisfactory results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Event-triggered adaptive neural inverse optimal output-feedback control of steer-by-wire vehicle systems with prescribed performance

This article addresses the event-based adaptive optimal fault-tolerant consensus control problem for a class of nonlinear multiagent systems (MASs) under a directed graph. It can be solved that both control gains and actuator failure parameters are unknown in considered MASs, which enhances the practicability of optimal consensus control. First, a reinforcement learning-based distributed optimal control law is designed by constructing the identifier-critic-actor learning networks. Furthermore, by utilizing the distributed optimal control law as an auxiliary variable, an adaptive fault-tolerant controller is proposed to effectively compensate for actuator failures. Meanwhile, a co-design scheme is proposed for the construction of an event-triggered control input with the fault-tolerant property. It is proven that the designed control input ensures the boundedness of closed-loop systems through rigorous stability analysis. Finally, the effectiveness of the developed approach can be illustrated via simulations of numerical nonlinear MASs and a group of autonomous underwater vehicles.

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

In this paper, by employing an online algorithm based on policy iteration (PI), an adaptive optimal control problem for continuous-time (CT) nonlinear partially uncertain dynamic systems is investigated. In this proposed algorithm, a discounted cost function is discussed, which is considered to be a more general case for optimal control problems. Two neural networks (NNs) are used to implement the algorithm, which aims at approximating the cost function and the control law, respectively. The uniform convergence to the optimal control is proven, and the stability of the system is guaranteed. An illustrating example is given.

The optimal control with an ergodic cost function is investigated for a class of stochastic discrete‐time linear systems with unknown system coefficient matrices. We present an online value iteration‐based stochastic adaptive dynamic programming algorithm to obtain the approximation sequence of the optimal state feedback control gain and rigorously prove that the approximation sequence converges to the optimal state feedback control gain under some reasonable conditions. In the framework of direct adaptive control, the diminishing excitation technique is introduced for an unknown stochastic discrete‐time state space model, and we prove that the adaptive controller, which is given by real‐time computation, is optimal. In contrast to existing related results, our method does not need to collect enough data to solve the Bellman equation in each iteration and avoids the requirement to estimate means and variances of controllers or states. A numerical simulation is provided to evaluate the efficacy of the presented approach.

Optimal adaptive control of fed-batch fermentation processes