Discrete‐Valued Model Predictive Control Using Sum‐of‐Absolute‐Values Optimization

In this paper, we propose a new design method of discrete‐valued model predictive control for continuous‐time linear time‐invariant systems based on sum‐of‐absolute‐values (SOAV) optimization. The finite‐horizon discrete‐valued control design is formulated as an SOAV optimal control, which is an expansion of L¹ optimal control. It is known that under the normality assumption, the SOAV optimal control exists and takes values in a fixed finite alphabet set if the initial state lies in a subset of the reachable set. In this paper, we analyze the existence and discreteness property for systems that do not necessarily satisfy the normality assumption. Then, we extend the finite‐horizon SOAV optimal control to infinite‐horizon model predictive control (MPC). We give sufficient conditions for the recursive feasibility and the stability of the MPC‐based feedback system in the presence of bounded noise. Simulation results show the effectiveness of the proposed method.     

Intersample ripple‐free multirate optimal controller design

A systematic approach for the design of multirate controllers resulting in closed loops free of intersample ripple is proposed. The approach is particularly suited for design frameworks such as optimal control for which previous proposed conditions to eliminate intersample ripple cannot be readily incorporated. It is based on transforming the control inputs in the lifted transfer matrix of the design plant in a manner that stabilizing controllers for the transformed plant are in one‐to‐one correspondence with stabilizing ripple‐free controllers for the original plant. Thus, no solutions are lost in the process of this transformation and a general stability result is obtained that can be also used in other multirate controller design methodologies to achieve ripple‐free response. The results do not require that the plant should be open‐loop stable and in particular can contain integrating instabilities. Copyright © 2012 John Wiley & Sons, Ltd.     

Closed‐form solution to finite‐horizon suboptimal control of nonlinear systems

Finite‐horizon optimal control of input‐affine nonlinear systems with fixed final time is considered in this study. It is first shown that the associated Hamilton–Jacobi–Bellman partial differential equation to the problem is reducible to a state‐dependent differential Riccati equation after some approximations. With a truncation in the control equation, a near optimal solution to the problem is obtained, and the global onvergence properties of the closed‐loop system are analyzed. Afterwards, an approximate method, called Finite‐horizon State‐Dependent Riccati Equation (Finite‐SDRE), is suggested for solving the differential Riccati equation, which renders the origin a locally exponentially stable point. The proposed method provides online feedback solution for controlling different initial conditions. Finally, through some examples, the performance of the resulting controller in finite‐horizon control is analyzed. Copyright © 2014 John Wiley & Sons, Ltd.     

Iterative ‐conic controller synthesis

This paper proposes a method to synthesize controllers that minimize an upper bound on the closed‐loop ‐norm while imposing desired controller conic bounds. An initial conic controller is synthesized and iteratively improved. Conic sectors can be used to characterize a variety of input‐output properties, such as gain, phase, and minimum gain. If such plant properties hold robustly to uncertainty present, then closed‐loop stability can be ensured robustly via the Conic Sector Theorem by imposing desired controller conic bounds. Consequently, this paper provides a versatile optimal and robust controller synthesis method. Moreover, it relies only on the solution of convex optimization problems subject to linear matrix inequality constraints, making it readily implementable.     

Decomposition of the min–max multi‐model problem via integral sliding mode

The concept of the integral sliding mode (ISM) is revised and applied for robustification of a linear time invariant min–max multi‐model problem with uncertainties. Modified version of ISM ensures the insensitivity of the designed min–max control law with respect to matched uncertainty, starting from the beginning of the process, and guarantees that the unmatched part of uncertainties is minimized and not amplified. Proposed ISM dynamics allows to reduce the dimension [Nn] of the min–max control design problem to the space of unmatched uncertainties only of [Nn?(N?1)m] size. A numerical example illustrates that the suggested modification of the ISM dynamics does not change the min–max control as well as the value of the corresponding performance index. Copyright © 2005 John Wiley & Sons, Ltd.     

Swing‐Stabilization Up for a Rotatory‐Elastic Pendulum Via Nonlinear Sub‐Optimal Control

This paper deals with the smooth control design for Swing‐Stabilization Up of underactuated pendular robot. The considered system has, at least, two different no actuated links, one of them is pendular like elbow, the other one is prismatic and elastic. Thus, the control aim is to swing‐up and stabilize the underactuated system by using non‐switched control algorithm. To this, the control algorithm summarizes the concept of sub‐optimal control, the energy based control and the Kalman's canonical decomposition to unify the Swing‐Up and Stabilization of the considered underactuated system. In order to test the designed control algorithm, experimental results are presented for the non‐conventional rotatory elastic‐pendulum system.     

Performance‐based near‐optimal vibration control for nonlinear offshore platforms with delayed input

This paper investigates the vibration control problem for offshore platform, where the nonlinear characteristics, delayed input and external wave force are considered in time domain. By introducing a delay‐free reconstructional vector and applying the maximum principle, the original vibration problem for offshore platform is formulated as a nonlinear two‐point‐boundary‐value (TPBV) problem with delayed items. The major contribution of this paper is that a performance‐based near‐optimal vibration control strategy is proposed by solving this nonlinear TPBV problem, which includes a feedback item with offshore platform system state, a feedforward item with wave force state, and a compensator for nonlinear and delayed items with infinite supersensitive component. In particular, the designed compensator is calculated from two group series of linear differential equations by introducing a parameter for expending the Maclaurin series of nonlinear and delay items. Meanwhile, an iterative algorithm is designed to make the proposed vibration control scheme computable based on the control performance in each iterative procedure. Finally, experimental results show that the displacement, velocity and performance index of an employed offshore platform achieved small values under the proposed control strategy and designed algorithm.     

Surrogate‐based methods for black‐box optimization

In this paper, we survey methods that are currently used in black‐box optimization, that is, the kind of problems whose objective functions are very expensive to evaluate and no analytical or derivative information is available. We concentrate on a particular family of methods, in which surrogate (or meta) models are iteratively constructed and used to search for global solutions.     

Computationally‐Light Non‐Lifted Data‐Driven Norm‐Optimal Iterative Learning Control

Computational complexity and model dependence are two significant limitations on lifted norm optimal iterative learning control (NOILC). To overcome these two issues and retain monotonic convergence in iteration, this paper proposes a computationally‐efficient non‐lifted NOILC strategy for nonlinear discrete‐time systems via a data‐driven approach. First, an iteration‐dependent linear representation of the controlled nonlinear process is introduced by using a dynamical linearization method in the iteration direction. The non‐lifted NOILC is then proposed by utilizing the input and output measurements only, instead of relying on an explicit model of the plant. The computational complexity is reduced by avoiding matrix operation in the learning law. This greatly facilitates its practical application potential. The proposed control law executes in real‐time and utilizes more control information at previous time instants within the same iteration, which can help improve the control performance. The effectiveness of the non‐lifted data‐driven NOILC is demonstrated by rigorous analysis along with a simulation on a batch chemical reaction process.     

TWO‐DEGREE‐OF‐FREEDOM CONTROL SCHEME FOR PROCESSES WITH LARGE TIME DELAY

In this paper, an analytical two‐degree‐of‐freedom‐control scheme is proposed for controlling processes with large time delay. The main contributions of this paper are that a setpoint response controller and an H_∞ PID load‐loop controller are developed based on optimal control theory, and control parameters are derived analytically. This structure can also be used to control integrating or unstable processes.     

Linear‐Quadratic Optimal Control Problems for Mean‐Field Stochastic Differential Equations with Jumps

In this paper, we study a linear‐quadratic optimal control problem for mean‐field stochastic differential equations driven by a Poisson random martingale measure and a one‐dimensional Brownian motion. Firstly, the existence and uniqueness of the optimal control is obtained by the classic convex variation principle. Secondly, by the duality method, the optimality system, also called the stochastic Hamilton system which turns out to be a linear fully coupled mean‐field forward‐backward stochastic differential equation with jumps, is derived to characterize the optimal control. Thirdly, applying a decoupling technique, we establish the connection between two Riccati equations and the stochastic Hamilton system and then prove the optimal control has a state feedback representation.     

Determination Of The Phase Current Waveform For A Disc‐Type Axial‐Flux Wheel Motor

An optimal design of the driving current pattern for a disc‐type axial‐flux brushless DC wheel motor of an electric vehicle is proposed in this paper. The electro‐magnetic dynamic model of the motor is established with magnetic circuits, describing the relationship between the output torque and excitation current. The optimal current pattern, in terms of magnitude and phase angle, is then obtained by maximizing the output torque with respect to the rotor shift. Compared with the traditional three‐phase‐on current pattern of fixed 120–degree phase shift, both the average torque and efficiency with the driving current of an optimal advanced switching angle are seen to be improved under various loading conditions. The motor performance with the optimal driving waveform is simulated and verified by experiments.     

Finite‐Time Optimal Formation Control for Second‐Order Multiagent Systems

This paper studies the problem of finite‐time optimal formation control for second‐order multiagent systems in situations where the formation time and/or the cost function need to be considered. The finite‐time optimal formation control laws are proposed for the cases with or without a leader, respectively. For the case of control being constrained, the time optimal formation problem is considered and an algorithm is designed to derive a feasible solution for the problem concerned. Although the feasible solution may not be optimal, it can provide a lower bound for time for the formation problem with control constraints. Once the given formation time is lower than this bound, the control constraints cannot be ensured. Finally, some numerical examples are given to illustrate the effectiveness of the theoretical results.     

Event‐triggered optimal tracking control of nonlinear systems

We propose a novel event‐triggered optimal tracking control algorithm for nonlinear systems with an infinite horizon discounted cost. The problem is formulated by appropriately augmenting the system and the reference dynamics and then using ideas from reinforcement learning to provide a solution. Namely, a critic network is used to estimate the optimal cost while an actor network is used to approximate the optimal event‐triggered controller. Because the actor network updates only when an event occurs, we shall use a zero‐order hold along with appropriate tuning laws to encounter for this behavior. Because we have dynamics that evolve in continuous and discrete time, we write the closed‐loop system as an impulsive model and prove asymptotic stability of the equilibrium point and Zeno behavior exclusion. Simulation results of a helicopter, a one‐link rigid robot under gravitation field, and a controlled Van‐der‐Pol oscillator are presented to show the efficacy of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Global Optimal Feedback‐Linearizing Control of Robot Manipulators

The present paper offers a new optimal feedback‐linearizing control scheme for robot manipulators. The method presented aims at solving a special form of the unconstrained optimal control problem (OCP) of robot manipulators globally using the results of the Lyaponov method and feedback‐linearizing strategy and without using the calculus of variations (indirect method), direct methods, or the dynamic programming approach. Most of these methods and their sub‐branches yield a local optimal solution for the considered OCP by satisfying some necessary conditions to find the stationary point of the considered cost functional. In addition, the proposed method can be used for both set‐point regulating (point‐to‐point) tasks (e.g. pick‐and‐place operation or spot welding tasks) and trajectory tracking tasks such as painting or welding tasks. However, the proposed method can not support the physical constraints on robot manipulators and requires precise dynamics of the robot, as well. Instead, it can be used as an on‐line optimal control algorithm which produces the optimal solution without performing any kind of optimization algorithms which require time to find the optimal solution.     

Non‐metamerism of boundary colors in multi‐primary displays

Abstract— A control sequence gives the intensities of the primaries for a pixel of a display device. The display gamut, i.e., the set of all the colors that a display can produce, is a zonohedral subset of CIE XYZ space and contains both boundary and interior colors. Displays with four primaries or more exhibit metamerism, in which different control sequences produce colors that appear identical to an observer. This paper shows mathematically that, provided no three primaries are linearly dependent, metamerism can only occur for interior colors. When there are four or more primaries, metamers can always be found for interior colors. A color on the gamut boundary, by contrast, is only produced by a unique control sequence. The proof used for displays can be extended to object‐color solids, to show that optimal colors, which are on the boundary of an object‐color solid, have unique reflectance functions.     

Vertical vibration control of an in‐wheel motor‐driven electric vehicle using an in‐wheel active vibration system

The objective of this study is to present a novel in‐wheel (IW) active vibration system for an IW motor (IWM)‐driven electric vehicle to overcome the negative effects of vertical vibration due to road roughness and the impact of rotary inertial forces from the IWM. First, the reason for the poor ride comfort of the general electric wheel structure is examined by theoretical derivation. Second, a 6 degree‐of‐freedom (DOF) vehicle model is established and the corresponding cost function based on 10 ride comfort indexes is proposed. Third, a fuzzy optimal sliding mode (FOSM) control method is presented and the IW active vibration system is designed by applying this proposed control theory. Then, normalization and analytic hierarchy process (AHP) methodologies are adopted to select reasonable weighted coefficients of performance indexes. Finally, the advantages of the electric vehicle with the IW active vibration system are illustrated by MATLAB/Simulink. Analysis results demonstrate the feasibility and effectiveness of the proposed method.     

LQR‐based optimal topology of leader‐following consensus

In this paper, we consider the optimal topology for leader‐following consensus problem of continuous‐time and discrete‐time multi‐agent systems based on linear quadratic regulator theory. For the first‐order multi‐agent systems, we propose a quadratic cost function, which is independent of the interaction graph, and find that the optimal topology is a star topology. For the second‐order multi‐agent systems, a quadratic cost function is also constructed, whereas the optimal topology for second‐order leader‐following consensus problem is an unevenly weighted star topology. The universality of these findings means that if each follower is connected with the leader, the information exchange between followers is unnecessary and insufficient. Simulation examples are provided to illustrate the effectiveness of the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Smart‐Bogie: Semi‐Active Lateral Control of Railway Vehicles

The topic of this paper is the design and analysis of a control system for the lateral movement of the carbody in a train. The control system is implemented via semi‐active electro‐hydraulic dampers located on the secondary‐suspension that links the bogie to the structure of the carbody of the train. The entire design procedure is outlined: the semi‐active damper is accurately modeled; using the actuator model, the control strategies are implemented and tuned on a vehicle simulator; the best control strategies then are implemented and tested on a realistic laboratory test‐bench, which accurately reproduces the lateral dynamics of a train. A wide range of semi‐active control strategies is tested. Among them, the best performing and most efficient is a recently‐proposed strategy which requires only a single sensor located cabin‐side.