Quadratic Optimal Control Research Articles

Linear quadratic optimal control of a high-performance loudspeaker

Linear quadratic optimal control of a high-performance loudspeaker

Approximate Solution for Some Continuous Optimal Control Problems Using Veita-Pell Polynomials

In this paper, Veita-Pell polynomials (VPPs) are first presented with some interesting properties. These properties are utilized to construct a general explicit formula of their operational matrix of derivative. Then an appropriate direct technique is suggested for solving quadratic optimal control problems based on VPPs and the idea of state parameterization algorithm. The resulting performance index optimal value shows the proposed method is able to provide a good treatment with fast convergence. The effectiveness of the presented method is illustrated by solving three numerical examples. The obtained results show that as the number of basis functions VPPs increase the error in the solution by the present method will be decreased and it may exactly close with the analytical one. This is the main modification of the algorithm and this contribution in the using special basis functions in obtaining an approximate solution with minimum number of VPPs and satisfactory accuracy.

Stochastic Linear Quadratic Optimal Control of Speed and Position of Multiple Trains on a Single-Track Line

Stochastic Linear Quadratic Optimal Control of Speed and Position of Multiple Trains on a Single-Track Line

The mean‐field linear quadratic optimal control problem for stochastic systems controlled by impulses

AbstractIn the present note, we state and solve the linear quadratic (LQ) control problem for a class of McKean–Vlasov stochastic differential equations for which the control actions are of impulsive nature. After reformulating the original optimization problem using an orthogonal decomposition of the state variables, we introduce an adequately defined system of two coupled matrix Lyapunov‐type differential equations with jumps. Such equations are central for the definition of the optimal feedback gains corresponding to the closed‐loop representation of the optimal LQ control.

Comprehensive Semi-Analytical Approach to Quadratic Optimal Control Problems Governed by Ordinary Differential Equations

Comprehensive Semi-Analytical Approach to Quadratic Optimal Control Problems Governed by Ordinary Differential Equations

Indefinite linear quadratic optimal control problem for uncertain random discrete-time systems

Indefinite linear quadratic optimal control problem for uncertain random discrete-time systems

Stochastic linear quadratic optimal control problems with expectation-type linear equality constraints on the terminal states

A stochastic linear quadratic (LQ) optimal control problem with an expectation-type linear equality constraint on the terminal state is considered. Under the solvability condition on a stochastic Riccati equation and a surjectivity condition on the linear constraint mapping, the constrained stochastic LQ problem is solved completely by the Lagrangian duality theory. Some equivalent characterizations of the surjectivity condition are discussed by the controllability theory of linear control systems. Especially, the equivalence between the surjectivity condition and a Kalman-type rank condition is proved under proper conditions.

Research on road tracking and anti-roll game control scheme of commercial vehicle based on Nash equilibrium

In view of the problem that the active suspension conflicts with the road tracking system while resisting roll when the commercial vehicle encounters emergency road conditions in the process of unmanned driving, this article is based on the Nash non-cooperative open-loop feedback game theory, taking the road tracking system, and the active anti-roll system as the participants of the game. An interactive control scheme which can not only accurately steer but also take into account the vertical roll stability is proposed. Firstly, the coupled model of Horizontal pendulum-anti-roll for commercial vehicles is established and extended to the vehicle-road three-degree of freedom closed model. Then, based on the derivation of the linear quadratic optimal control model (LQ), the non-cooperative open-loop Nash game theory is used to obtain the interactive optimal control afferent the road tracking system and the active anti-roll system. Finally, the experimental scheme is verified by hardware in the loop experiment. The results show that the interactive control scheme of road tracking and anti-roll based on Nash non-cooperative game for commercial vehicles allows the vehicle to take the vertical stability into account while turning actively, thus ensuring the safety and stability of the vehicle during driving.

Linear quadratic optimal control for time-delay stochastic system with partial information

ABSTRACT This paper is concerned with the linear quadratic optimal control problem for the time-delay stochastic system with partial information. The main contribution is to derive the equivalent solvability condition and give the explicitly optimal controller under partial information in terms of the Riccati equations. The key is to explicitly solve the forward and backward stochastic difference equations with partial information, which is derived from the stochastic maximum principle.

Linear quadratic optimal regulation for multiplicative noise systems with special terminal penalty

This paper focuses on the linear quadratic optimal control problem for stochastic systems with a special terminal penalty. The specialty lies in that the terminal penalty is a quadratic term over the conditional expectations of the terminal state. The essential difficulty lies in an additional measurability constraint on the input induced by the conditional expectation term, which is shared by the control problems for the stochastic system with delays, rational expectations problems, control problems involving conditional expectation terms, asymmetric information control and so on. A new idea, dynamic programming combined with orthogonal decomposition, is proposed to deal with this problem. The orthogonal decomposition eliminates the additional measurability constraint on the input. The solvability condition and the optimal controller are obtained by developing generalised Riccati equations. Numerical experiment is provided to support the achieved results.

Stochastic Linear-Quadratic Optimal Control with Partial Observation

This paper studies a class of quadratic optimal control problems for partially observable linear dynamical systems. In contrast to the full information case, the control is required to be adapted to the filtration generated by the observation system, which in turn is influenced by the control. The variation method fails in this case due to the fact that the filtration is not fixed. To overcome the difficulty, we use the orthogonal decomposition of the state process to write the cost functional as the sum of two parts: one is a functional of the control and the filtering process and the other part is independent of the choice of the control. The first part possesses a mathematical structure similar to the full information problem. By completing the square, it is shown that the open-loop optimal control is given by a feedback representation via the filtering process. The optimal value is also obtained explicitly.

Convergence rates of a discrete feedback control arising in mean-field linear quadraticoptimal control problems

Convergence rates of a discrete feedback control arising in mean-field linear quadraticoptimal control problems

The Global Maximum Principle for Progressive Optimal Control of Partially Observed Forward-Backward Stochastic Systems with Random Jumps

This paper is concerned with a partially observed progressive optimal control problem of forward-backward stochastic differential equations with random jumps, where the control domain is not necessarily convex, and the control variable enters into all the coefficients. In our model, the observation equation is not only driven by a Brownian motion but also a Poisson random measure, which also has correlated noises with the state equation. The partially observed global maximum principle is proved. To show its applications, a partially observed linear quadratic progressive optimal control problem of forward-backward stochastic differential equations with random jumps is investigated by the maximum principle and stochastic filtering. State estimate feedback representation of the optimal control is given in a more explicit form by introducing some ordinary differential equations.

Feedback-based fault-tolerant and health-adaptive optimal charging of batteries

The key technology barriers that hinder the growth of Electric Vehicles (EVs) are long charging time, the shorter life-time of EV batteries, and battery safety. Specifically, EV charging protocols have significant effects on battery lifetime and safety. If not charged properly, the battery could end up with shorter life, and more importantly, improper charging can cause battery faults leading to catastrophic failures. To overcome these barriers, we propose a closed-loop feedback based approach, that enables real-time optimal fast charging protocol adaptation to battery health and possess active diagnostic capabilities in the sense that, during charging, it detects real-time faults and takes corrective action to mitigate such fault effects. We utilize battery electrical–thermal model, explicit battery capacity and power fade aging models, and thermal fault model to capture battery behavior. In conjunction with the models, we adopt linear quadratic optimal control techniques to realize the feedback-based control algorithm. Simulation studies are presented to illustrate the effectiveness of the proposed scheme.

Value Iteration for Continuous-Time Linear Time-Invariant Systems

Two data-driven strategies for value iteration in linear quadratic optimal control problems over an infinite horizon are proposed. The two architectures share common features, since they both consist of a purely continuous-time control architecture and are based on the forward integration of the Differential Riccati Equation (DRE). They profoundly differ, instead, in the estimation mechanism of the vector field of the underlying DRE from collected data: the first relies on a characterization of properties of the advantage function associated to the problem, whereas the second is inspired by tools from adaptive control theory and ensures semi-global exponential convergence to the optimal solution. Advantages and drawbacks of the architectures are discussed, while the performance is validated via a benchmark numerical example.

The new solution bounds of the discrete algebraic Riccati equation and their applications in redundant control inputs systems

AbstractRedundant control inputs play an important part in engineering and are often used in control problems, dynamic control allocation, quadratic performance optimal control, and many uncertain systems. In this paper, by the equivalent form of the discrete algebraic Riccati equation (DARE), we propose new upper and lower bounds of the solution for the equivalent DARE. Compared with some existing work on this topic, the new bounds are more tighter. Next, when increasing the columns of the input matrix, we give the applications of these new upper and lower solution bounds to obtain a sufficient condition for strictly decreasing feedback controller gain. Finally, corresponding numerical examples illustrate the effectiveness of our results.

On the stochastic linear quadratic optimal control problem by piecewise constant controls: The infinite horizon time case

This paper is devoted to the problem of indefinite stochastic linear quadratic (LQ) optimal control by piecewise constant controls in an infinite horizon case. By restricting the set of admissible controls to the class of piecewise constant stochastic processes, we reformulated the above control problem under the setting of systems modeled by Itô differential equations controlled by impulses. We show that the solution in a state feedback form of the indefinite stochastic LQ control problem is equivalent to the existence of a global stabilizing solution associated to a class of backward matrix linear differential equations with a Riccati type jumping operators.

Simulation and Experiment of Active Vibration Control Based on Flexible Piezoelectric MFC Composed of PZT and PI Layer.

In order to improve the vibration suppression effect of the flexible beam system, active control based on soft piezoelectric macro-fiber composites (MFCs) consisting of polyimide (PI) sheet and lead zirconate titanate (PZT) is used to reduce the vibration. The vibration control system is composed of a flexible beam, a sensing piezoelectric MFC plate, and an actuated piezoelectric MFC plate. The dynamic coupling model of the flexible beam system is established according to the theory of structural mechanics and the piezoelectric stress equation. A linear quadratic optimal controller (LQR) is designed based on the optimal control theory. An optimization method, designed based on a differential evolution algorithm, is utilized for the selection of weighted matrix Q. Additionally, according to theoretical research, an experimental platform is built, and vibration active control experiments are carried out on piezoelectric flexible beams under conditions of instantaneous disturbance and continuous disturbance. The results show that the vibration of flexible beams is effectively suppressed under different disturbances. The amplitudes of the piezoelectric flexible beams are reduced by 94.4% and 65.4% under the conditions of instantaneous and continuous disturbances with LQR control.

An adaptive dynamic programming-based algorithm for infinite-horizon linear quadratic stochastic optimal control problems

An adaptive dynamic programming-based algorithm for infinite-horizon linear quadratic stochastic optimal control problems

Policy Optimization for Markovian Jump Linear Quadratic Control: Gradient Method and Global Convergence

Recently, policy optimization has received renewed attention from the control community due to various applications in reinforcement learning tasks. In this article, we investigate the global convergence of the gradient method for quadratic optimal control of discrete-time Markovian jump linear systems (MJLS). First, we study the optimization landscape of direct policy optimization for MJLS, with static-state feedback controllers and quadratic performance costs. Despite the nonconvexity of the resultant problem, we are still able to identify several useful properties such as coercivity, gradient dominance, and smoothness. Based on these properties, we prove that the gradient method converges to the optimal-state feedback controller for MJLS at a linear rate if initialized at a controller, which is mean-square stabilizing. This article brings new insights for understanding the performance of the policy gradient method on the Markovian jump linear quadratic control problem.