Suboptimal Control Method Research Articles

Steering control for handling and stability and wear resistance of multi-axle vehicles

The steering performance of a vehicle directly affects its handling and stability, and tire wear during steering. For multi-axle vehicles equipped with a mechanical hydraulic steering system (MHS), this paper describes a steering-by-wire hydraulic system (SHS) for a third axle that can reduce the steering wear of third-axle tires while improving the handling and stability. A hydraulic steering system based on a reliable self-locking alignment cylinder was designed in this study, and a nonlinear dynamics model of a multi-axle vehicle was developed. In terms of the control strategy, the upper controller was a decision selector with a lateral acceleration threshold of 0.3 g , at which point the system entered the nonlinear kinematic state as a criterion for decision-making. The suboptimal linear time-varying model predictive control (S-LTV-MPC) method or Ackermann steering theory was used to calculate the target steering angle of the third axle. The lower controller was a fuzzy proportional–integral–derivative controller for tracking the steering angle of the third axle. The simulation and test results showed that the S-LTV-MPC method can meet the requirements of real-time control and accuracy. The designed SHS exhibited good handling and stability, and anti-wear properties during steering.

A method for Sub-optimal control of the delayed fractional order linear time varying systems with computation reduction approach

A method for Sub-optimal control of the delayed fractional order linear time varying systems with computation reduction approach

Sub-optimal fixed-finite-horizon spacecraft configuration control on SE(3)

For achieving the desired configuration of spacecraft at the desired fixed time, a sub-optimal fixed-finite-horizon configuration control method on the Lie group SE(3) is developed based on the Model Predictive Static Programming (MPSP). The MPSP technique has been widely used to solve finite-horizon optimal control problems and is known for its high computational efficiency thanks to the closed-form solution, but it cannot be directly applied to systems on SE(3). The methodological innovation in this paper enables that the MPSP technique is extended to the geometric control on SE(3), using the variational principle, the left-invariant properties of Lie groups, and the topology structure of Lie algebra space. Moreover, the energy consumption, which is crucial for spacecraft operations, is considered as the objective function to be optimized in the optimal control formulation. The effectiveness of the designed sub-optimal control method is demonstrated through an online simulation under disturbances and state measurement errors.

Human–machine cooperative scheme for car-following control of the connected and automated vehicles

To address the out-of-the-loop problem of the automated driving, a human–machine cooperative scheme for car-following control of the connected and automated vehicles (CAVs) is proposed. The proposed scheme can keep the drivers always in the loop and improve the car-following performance. To be specific, the driving automation system (artificial driver) is assigned to the task of velocity tracking and the human driver is responsible for headway adjustment. For the velocity tracking task, a feedforward–feedback control strategy was designed firstly by considering the advantages of the accurate perception and communication of CAVs, then an H∞ suboptimal control method was developed to optimize the controller parameters according to the desired performance index, further the controller was fine-tuned based on the idea of human-simulated intelligent control (HSIC) to improve the dynamic performance of the velocity tracking. For the operator’s headway adjusting task, the stability analysis based on the Lyapunov function proved that the simple proportional feedback control can be assumed by the driver to ensure the system stability under the cooperation of automated velocity tracking. The experiments based on the driving simulator demonstrated that human–machine cooperative scheme for car-following can reduce the tracking error of vehicle distance effectively, and the human driver can be kept in the control loop with a smaller operating load.

Suboptimal control for nonlinear slow‐fast coupled systems using reinforcement learning and Takagi–Sugeno fuzzy methods

SummaryIn this article, by using singular perturbation theory, reinforcement learning (RL), and Takagi–Sugeno (T‐S) fuzzy methods, a RL‐fuzzy‐based composite suboptimal control method is proposed for nonlinear slow‐fast coupled systems (SFCSs) with unknown slow dynamics. First, the SFCSs is decomposed into slow and fast subsystems and the original optimal control problem is reduced to two subproblems. Then, for the slow subsystem, a nonlinear coordinate transformation is introduced to transform the nonquadratic slow utility function into the quadratic form. Unmeasurable virtual slow subsystem state is reconstructed by the state measurements of original system and slow controller design algorithm is proposed in the framework of RL by utilizing the actor‐critic neural networks to approximate the controller and cost function. For the fast subsystem, T‐S fuzzy model is established and state measurements of the original system are exploited to reconstruct the unmeasurable fast subsystem state. Fast controller is designed with the approach of parallel distributed compensation. The obtained slow and fast controllers form the composite suboptimal controller for the original SFCSs. Considering the state reconstruction error, convergence of the slow controller design algorithm, suboptimality of the composite controller, and stability of the closed‐loop SFCSs are analyzed. Finally, the effectiveness of our proposed method is illustrated by examples.

Periodic Event-Triggered Suboptimal Control With Sampling Period and Performance Analysis.

In this paper, the periodic event-triggered suboptimal control (PETSOC) method is developed for continuous-time linear systems. Different from event-triggered control, where the triggering condition is monitored continuously, the developed PETSOC method only verifies the triggering condition periodically at sampling instants, which further reduces computational resources. First, the control gain of the PETSOC is designed based on the algebraic Riccati equation. Subsequently, the periodic event-triggering condition is proposed for the suboptimal control method, which is only verified at sampling instants periodically. The sampling period is determined and analyzed based on the continuous form of the triggering condition. Moreover, the stability and the performance upper bound of the closed-loop system with the PETSOC are proved. Finally, the effectiveness of the developed PETSOC is validated through simulation on an unstable batch reactor.

Nonlinear sliding sector design for multi‐input systems with application to helicopter control

SummaryThe ability of helicopters to hover and land vertically has spurred an interesting field of research on the development of autonomous flight for these rotatory wing aircrafts. Linear control theory with gain scheduling, which is based on linearizing the system at the equilibrium points, dominated the helicopter autopilot design. Unlike the linear cascaded autopilot structure used in the existing literature, this paper uses state‐dependent linear like structure, including rate‐limited actuator dynamics, with cascaded autopilot topology. This approach allows nonlinear control laws to be implemented throughout the entire flight envelope, providing satisfactory robustness and stability over the various parameter uncertainties and time delays. The cascaded autopilot topology with nonlinear dynamical equations contains a new sliding sector control (SSC) mechanism which is derived for multi‐input nonlinear dynamical systems. The proposed SSC structure for multi‐input nonlinear systems is used in the inner loop of the cascaded autopilot system where the fastest dynamics are required to be controlled for rapid changes in the helicopter dynamical characteristics which enables one to stabilize the helicopter over a wide range of flight conditions. The proposed cascaded autopilot topology with the new SSC mechanism is tested in simulations to assess its robustness and stability properties. To establish its feasibility, the proposed control method is replaced with a suboptimal control method, namely state‐dependent differential Riccati equation (SDDRE) method, for the inner loop and the results of the proposed control architecture are compared with those of SDDRE method.

Adaptive composite suboptimal control for linear singularly perturbed systems with unknown slow dynamics

SummaryIn this article, using singular perturbation theory and adaptive dynamic programming (ADP) approach, an adaptive composite suboptimal control method is proposed for linear singularly perturbed systems (SPSs) with unknown slow dynamics. First, the system is decomposed into fast‐ and slow‐subsystems and the original optimal control problem is reduced to two subproblems in different time‐scales. Afterward, the fast subproblem is solved based on the known model of the fast‐subsystem and a fast optimal control law is designed by solving the algebraic Riccati equation corresponding to the fast‐subsystem. Then, the slow subproblem is reformulated by introducing a system transformation for the slow‐subsystem. An online learning algorithm is proposed to design a slow optimal control law by using the information of the original system state in the framework of ADP. As a result, the obtained fast and slow optimal control laws constitute the adaptive composite suboptimal control law for the original SPSs. Furthermore, convergence of the learning algorithm, suboptimality of the adaptive composite suboptimal control law and stability of the whole closed‐loop system are analyzed by singular perturbation theory. Finally, a numerical example is given to show the feasibility and effectiveness of the proposed methods.

Chaos prediction and control based on time series analysis

The nonlinear time-series analysis method is used to study the nonlinear large-scale measurement system and the discrete nonlinear system. For the instability of the linear steady-scale large-scale pulse system, a class of discrete Lipschitz nonlinear system dimensionality observer is used. The suboptimal control method for chaotic discrete systems with time-delay is obtained. The mathematical model of the large-scale pulsed system and the nonlinear discrete system is established. The instability of the large-scale steady-turbulence-type impulsive large-scale system is discussed by using the concept of the metric impulse system. The chaos of the nonlinear large-scale pulsating large-scale system with perturbation is proved by using the Lyapunov V function and the comparison principle. Bifurcation, using differential dynamic programming method to transform the suboptimal control problem of nonlinear discrete systems with time delay into the optimal control problem of nonlinear discrete systems without time delay, and realize the control of chaos.

An iterative method for suboptimal control of a class of nonlinear time-delayed systems

ABSTRACTThis work presents an approximate solution method for the infinite-horizon nonlinear time-delay optimal control problem. A variational iteration method (VIM) is applied to design feedforward and feedback optimal controllers. By using the VIM, the original optimal control is transformed into a sequence of nonhomogeneous linear two-point boundary value problems (TPBVPs). The existence and uniqueness of the optimal control law are proved. The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoint vector sequence. The feedback term is determined by solving Riccati matrix differential equation. By using the finite-step iteration of a nonlinear compensation sequence, we can obtain a suboptimal control law. Simulation results demonstrate the validity and applicability of the VIM.

A Suboptimal Dual Control Method for the Stochastic Systems with Parameters Drifting

AbstractThis paper proposed a suboptimal dual control method for the stochastic systems with parameters drifting. Based on the consideration of the performance index control and the parameter estimation, the minimum variance of the system output and the estimated covariance matrix of the parameters estimation are both put into the performance index to evaluate the control quality. Furthermore, a dual control strategy is designed which is of the property of learning and control. Simulation results illustrate the effectiveness of the algorithm.

A Discontinuous Galerkin Method for optimal and sub-optimal control applied to an oscillating water column wave energy converter

This paper applies a Discontinuous Galerkin (DG) finite element time-stepping method for the numerical solution of optimal and sub-optimal control problems within the framework of the Pontryagin’s Maximum Principle. The local nature of the piecewise polynomial approximation used in the DG method handles easily the case of a large number of switching instants not known a priori. The weakly enforced inter-element continuity allows a simple implementation of element-wise mesh and polynomial refinement. To show the capabilities of the method, an element-wise time-interval refinement algorithm was implemented (the so-called h-refinement) and applied to a classic bang-bang optimal control problem. Finally, the application of the method to a practical problem is discussed: the optimal latching (bang-bang) control of a floating oscillating water column wave energy converter equipped with a self-rectifying air-turbine. The results presented in this study show that the DG method is an efficient alternative to the well-known Pseudo-Spectral methods.

An iterative method for suboptimal control of linear time-delayed systems

This article presents a new approach for solving the Optimal Control Problem (OCP) of linear time-delay systems with a quadratic cost functional. The proposed method can also be used for designing optimal control time-delay systems with disturbance. In this study, the Variational Iteration Method (VIM) is employed to convert the original Time-Delay Optimal Control Problem (TDOCP) into a sequence of nonhomogeneous linear two-point boundary value problems (TPBVPs). The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoint vector sequence. The feedback term is determined by solving Riccati matrix differential equation. By using the finite-step iteration of a nonlinear compensation sequence, we can obtain a suboptimal control law. Finally, Illustrative examples are included to demonstrate the validity and applicability of the technique.

Global Adaptive Dynamic Programming for Continuous-Time Nonlinear Polynomial Systems

This paper presents a novel adaptive sub-optimal control method for continuous-time nonlinear polynomial systems from a perspective of adaptive dynamic programming (ADP). This is achieved by relaxing the problem of solving an Hamilton-Jacobi-Bellman (HJB) equation into an optimization problem, which is solved via a new policy iteration method. The proposed methodology distinguishes from previously known nonlinear ADP methods in that the neural network approximation is avoided and that the resultant control policy is globally stabilizing, instead of semiglobally or locally stabilizing. Furthermore, in the absence of the a prior knowledge of the system dynamics, an online learning method is devised to implement the proposed policy iteration technique by generalizing the current ADP theory. Finally, the proposed method is applied to a jet engine surge control problem.

Channel Estimation with Optimal Power Controls in Amplify-and-Forward Relay Networks

In this paper, we present a power control method of relay for improving a channel estimation performance in amplify-and-forward (AF) relay networks over frequency-selective fading channel. We first analyze a channel mean-square error (MSE) by imposing a power control effect on a simple (LS) channel estimation. Then, we find that there is a trade-off between the amplitude of power control and MSE performance. Moreover, we propose the optimal and suboptimal power control methods in order to resolve such a trade-off. Finally, the superiority of the proposed channel estimation with optimal power controls is verified through numerical simulations.

Robust Suboptimal Control of an Electro-Hydraulic System with Variable Supply Pressure

In this study, a robust H2 suboptimal control method is proposed for an electro-hydraulic system with variable supply pressure. The H2 suboptimal controller is designed to minimize the sum of a quadratic performance criterion and the H2 norm of the closed-loop transfer function from the white noise disturbance to the system state space variables. The genetic algorithm is used to select the weighting matrices of the quadratic performance criterion. In order to improve the robust performance, parameter uncertainties of the electro-hydraulic system are considered in the process of genetic search. Simulation results demonstrate the effectiveness of the proposed approach.

Robust H∞ suboptimal control based on effective informed adaptive particle swarm optimisation algorithm for proton exchange membrane fuel cell system

A novel robust H ∞ control strategy used to adjust the oxygen excess ratio on the cathode side for proton exchange membrane fuel cell (PEMFC) system is proposed. This robust H ∞ suboptimal control method is based on an effective informed adaptive particle swarm optimisation algorithm with better equilibrium characteristic between global search and local search. Owing to the existence of uncertainties and disturbances, the setup of objectives associated with various inequality constraints and the selection of weighting functions is considered as an optimisation problem in the framework of H ∞ mixed sensitivity and structure singular value analysis. The simulation results on the running process of an electrical vehicle demonstrate that this proposed method can maintain oxygen excess ratio better at the optimal operating point, so that the net output power from the PEMFC system could be increased with the decrease of the parasitic power. In comparison with prior control approaches from other researchers, the method addressed in this study has exhibited better robust performance in the presence of multiple uncertain parameters and disturbances. The feasibility and the validity of the robust H ∞ suboptimal control method proposed have been proven qualitatively from the experimental study.

A quasi-optimal sliding mode control scheme based on control Lyapunov function

In this paper, the sliding mode control (SMC) method is integrated with a nonlinear suboptimal control method based on control Lyapunov function (CLF). According to the system nominal part, a CLF is first constructed in general to facilitate the nonlinear optimal system design and Sontag's formula is used in particular to generate a suboptimal controller. To take system uncertainties into account, the SMC mechanism is designed based on the CLF. By integration, the suboptimal control and SMC are made to function in a complementary manner. When the system state is far away from the equilibrium and the system nominal part is predominant, the nonlinear optimal control part will govern the system response as well as drive the system state approach the equilibrium in an optimal fashion. On the contrary, when approaching the equilibrium such that system perturbations become the main factor, the SMC will take over the control task to warrant the desired robustness property and achieve precise control.

Dual Adaptive Controllers based on Partial Certainty Equivalence

AbstractThe article deals with the optimal control of a linear discrete stochastic state space system with uncertain parameters. The solution of this optimization problem leads to design of controllers with dual features. Because the closed-form solution is hardly attainable a suitable suboptimal approaches has to be used. Many of the simpler approaches restrict the control horizon only to one step ahead and thus suffer from the myopic behavior. One way how to overcome this restriction is to use the partial certainty equivalence approximation of the joint probability density functions. The goal of this paper is to present a comparison of suboptimal adaptive dual control methods employing this approximation.

Suboptimal feedback control of flow over a sphere

Abstract In this study, we control unsteady motion in the wake behind a sphere using a suboptimal feedback control method based on the sensing of surface pressure. The cost function to be reduced is the square of the difference between the potential-flow and real pressures at the sphere surface. The actuation velocity (blowing/suction) is obtained from the suboptimal feedback control procedure. The sensing and actuation on the whole surface of the sphere is considered. This is an ideal case but provides a clear understanding of the effect of suboptimal feedback control on the present flow. We choose four different Reynolds numbers, Re = 100, 250, 300, and 425, covering four different flow regimes (steady axisymmetric, steady planar–symmetric, unsteady planar–symmetric, and unsteady asymmetric flows, respectively). With the present control, the vortex shedding disappears for Re = 300 and 425 and the drag is significantly reduced for all the Reynolds numbers considered.