Robust Optimal Control Law Research Articles

Off‐policy reinforcement learning algorithm for robust optimal control of uncertain nonlinear systems

AbstractIn this article an optimal control scheme is proposed to solve robust control problem for matched and unmatched system. In the proposed optimal approach the value functions are designed such that the obtained optimal control law guarantees asymptotic stability of the uncertain nonlinear system. Since the proposed robust optimal control problem is not straightforward to solve, an off‐policy reinforcement‐learning algorithm based on neural networks approximation is developed to obtain robust optimal control law iteratively. The robust control law for matched uncertain systems can be achieved via proposed off‐policy learning algorithm without requiring exact knowledge of system's dynamics. The advantages of the proposed robust optimal controller are verified by comparative simulations on an uncertain model of a car suspension system and a mathematical nonlinear model.

Robust Trajectory Planning for Hypersonic Glide Vehicle with Parametric Uncertainties

A hybrid double-loop optimization algorithm combing particle swarm optimization (PSO) and nonintrusive polynomial chaos (NIPC) is proposed for solving the robust trajectory optimization of hypersonic glide vehicle (HGV) under uncertainties. In the outer loop, the PSO method searches globally for the robust optimal control law according to a penalized fitness function that contains the system robustness considerations. In the inner loop, uncertainty propagation of the stochastic system is performed using the NIPC method, to provide statistical moments for the iterative scheme of the PSO method in the outer loop. Only control variables are discretized, and the state constraints are satisfied implicitly through the numerical integration process, which reduces the number of decision variables as well as the huge amount of computation increased by NIPC. In the end, the robust optimal control law is achieved conveniently. Numerical simulations are carried out considering a classical time-optimal trajectory optimization problem of HGV with uncertainties in both initial states and aerodynamic coefficients. The results demonstrate the feasibility and effectiveness of the proposed method.

ROBUST OPTIMAL CONTROL IN NOT-COMPLETELY CONTROLLABLE LINEAR TIME-VARYING SYSTEMS

A linear-quadratic differential game related to robust control problems in linear time-varying systems is considered. We show that difficulties, which may arise in obtaining the solution of the game and the optimal control law, are related to the fact that the trajectories x(t) (where the state x = (x1, ..., xn)) of the controlled system may be exactly or approximately localized in the subspace of dimensionality less than n, under all possible bounded piecewise continuous control impacts acting on the inputs, provided that the initial vector x(t0) is fixed, x(t0) = x0. We demonstrate how to overcome these difficulties by using the solution D(t) of inverse matrix differential equation of Riccati type and the pseudo-inverse matrix D+(t). We establish new sufficient conditions for the existence of the saddle point. We show that the optimal control can be extended beyond conjugate points if D(t) ≥ 0. We also derive and prove new explicit formulae for robust optimal control law using the matrices D(t) and D+(t). With the use of the pseudo-inverse matrix D+(t) uncontrollable (or almost uncontrollable) components can be automatically eliminated in choosing robust optimal control. In this paper robust optimal control problems in linear time-varying systems are investigated in the finite-horizon case.

Min-max control of constrained uncertain discrete-time linear systems

For discrete-time uncertain linear systems with constraints on inputs and states, we develop an approach to determine state feedback controllers based on a min-max control formulation. Robustness is achieved against additive norm-bounded input disturbances and/or polyhedral parametric uncertainties in the state-space matrices. We show that the finite-horizon robust optimal control law is a continuous piecewise affine function of the state vector and can be calculated by solving a sequence of multiparametric linear programs. When the optimal control law is implemented in a receding horizon scheme, only a piecewise affine function needs to be evaluated on line at each time step. The technique computes the robust optimal feedback controller for a rather general class of systems with modest computational effort without needing to resort to gridding of the state-space.

A PARAMETRIC OPTIMISATION APPROACH FOR ROBUST MPC

In this paper an algorithm is presented for deriving the explicit robust model based optimal control law. The system is represented by linear, discrete-time, time-invariant model with constraints on control and state variables and a quadratic objective function. Using the fundamentals of flexibility analysis the algorithm proposed in this paper derives the robust optimal control law off-line as a function of the state of the process, thus eliminating the repetitive solution of on-line optimisation problems. Hence, the on-line implementation is reduced to a sequence of simple function evaluations. The key advantageous features of the algorithm are demonstrated via an illustrative example.