Simultaneous linear and anti-windup controller synthesis using multiobjective convex optimization

We present a method for the synthesis of a control law for input constrained linear systems that incorporates both a traditional linear output-feedback controller as well as a static anti-windup compensator. Unlike traditional two-step anti-windup controller designs in which the linear controller and anti-windup compensator are designed sequentially, our method synthesizes all controller parameters simultaneously. This one-step design retains the anti-windup structure, thus providing structurally ‘a priori’ compensation for saturation. We derive sufficient conditions for guaranteeing global quadratic stability and for satisfying multiple, possibly conflicting, performance objectives on the constrained and unconstrained closed-loop dynamics. The resulting synthesis problem is recast as an optimization over linear matrix inequalities (LMIs). We demonstrate the proposed method on a benchmark problem.     

Optimal dead-time compensator design for stable and integrating processes with time delay

Recently, a modified Smith predictor with a prefilter has been proposed for first-order stable and integrating processes with time delay. The paper is a further investigation on the empirical method. In this paper, an optimal design procedure is developed for the scheme. With respect to the proposed controller and corresponding processes with time delay, the closed-loop time domain responses are estimated quantitatively. The robustness of the closed-loop system is analyzed. Finally, a simple tuning rule is proposed, which allows to tune the controller for desired time domain properties such as overshoot and rise time, or frequency domain criteria such as stability margin and bandwidth.     

Stability margins of nonlinear receding-horizon control via inverse optimality

Using the nonlinear analog of the Fake Riccati equation developed for linear systems, we derive an inverse optimality result for several receding-horizon control schemes. This inverse optimality result unifies stability proofs and shows that receding-horizon control possesses the stability margins of optimal control laws.     

Explicit sub-optimal linear quadratic regulation with state and input constraints

Optimal feedback solutions to the infinite horizon LQR problem with state and input constraints based on receding horizon real-time quadratic programming are well known. In this paper we develop an explicit solution to the same problem, eliminating the need for real-time optimization. It is shown that the resulting feedback controller is piecewise linear. This explicit functional structure is exploited for efficient real-time implementation. A suboptimal strategy, based on a suboptimal choice of a finite horizon and imposing additional limitations on the allowed switching between active constraint sets on the horizon, is suggested in order to address the computer memory and processing capacity requirements of the explicit solution.     

一种次最优鲁棒调节器的设计方法

本文基于最优控制和极点配置理论,提出一种灵敏度低、动特性好的次最优鲁棒调节器设计法。它具有计算方便、结构简单的特点。     

约束非线性系统多变量最优控制研究

近年来,非线性规划算法在最优控制领域中正受到越来越多的关注。该文深人研究并实现了一种新的非线性规划算法——FSQP算法,该算法具有所有迭代点均处于可行域之内、收敛速度较快的特点。提出了一种基于FSQP算法的约束非线性系统最优控制方法。然后,运用该方法解决了带有约束的复杂非线性系统的多变量时间最优控制问题,并通过计算机仿真表明了该控制算法的可行性和良好的控制效果。     

Control of constrained linear systems using fast sampling rates

This paper addresses the problem of optimal control of constrained linear systems when fast sampling rates are utilised. We show that there exists a well-defined limit as the sampling rate increases. An immediate consequence of this result is the existence of a finite sampling period such that the achieved performance is arbitrarily close to the limiting performance.     

Design of an optimal series compensator based on DARMA model — The MIMO case

Design of an optimal series compensator for MIMO systems is considered in this paper using the DARMA form. The main purpose is to show how to find the smallest number of samples in each output channel to yield an optimal series compensator which is of the smallest possible order.     

Dual-mode Nonlinear MPC via Terminal Control Laws With Free-parameters

The paper presents a new dual-mode nonlinear model predictive control (NMPC) scheme for continuous-time nonlinear systems subject to constraints on the state and control. The idea of control Lyapunov functions for nonlinear systems is used to compute the terminal regions and terminal control laws with some free-parameters in the dual-mode NMPC framework. The parameters of the terminal controller are selected offline to estimate the terminal region as large as possible; and the parameters are optimized online to gain optimality of the terminal controller with respect to given cost functions. Then a dual-mode NMPC algorithm with varying time-horizon is formulated for the constrained system. Recursive feasibility and closed-loop stability of this NMPC are established. The example of a spring-cart is used to demonstrate the advantages of the presented scheme by comparing to the dual-mode NMPC via the linear quadratic regulator (LQR) method.      

Open-loop and closed-loop robust optimal control of batch processes using distributional and worst-case analysis

The recognition that optimal control trajectories for batch processes can be highly sensitive to model uncertainties has motivated the development of methods for explicitly addressing robustness during batch processes. This study explores the incorporation of robust performance analysis into open-loop and closed-loop optimal control design. Several types of robust performance objectives are investigated that incorporate worst-case or distributional robustness metrics for improving the robustness of batch control laws, where the distributional approach computes the distribution of the performance index caused by parameter uncertainty. The techniques are demonstrated on a batch crystallization process. A comprehensive comparison of the robust performance of the open-loop and closed-loop system is provided.     

Simultaneous stabilization with near-optimal model reference tracking

In this paper we consider the use of linear time-varying controllers for simultaneous stabilization and performance. We prove that for every finite set of plants, we can design a linear time-varying controller which provides not only closed-loop stability, but also near-optimal model reference tracking.     

Minimizing control variation in nonlinear optimal control

In any real system, changing the control signal from one value to another will usually cause wear and tear on the system’s actuators. Thus, when designing a control law, it is important to consider not just predicted system performance, but also the cost associated with changing the control action. This latter cost is almost always ignored in the optimal control literature. In this paper, we consider a class of optimal control problems in which the variation of the control signal is explicitly penalized in the cost function. We develop an effective computational method, based on the control parameterization approach and a novel transformation procedure, for solving this class of optimal control problems. We then apply our method to three example problems in fisheries, train control, and chemical engineering.     

Robust and optimal predictive control of the COVID-19 outbreak

We investigate adaptive strategies to robustly and optimally control the COVID-19 pandemic via social distancing measures based on the example of Germany. Our goal is to minimize the number of fatalities over the course of two years without inducing excessive social costs. We consider a tailored model of the German COVID-19 outbreak with different parameter sets to design and validate our approach. Our analysis reveals that an open-loop optimal control policy can significantly decrease the number of fatalities when compared to simpler policies under the assumption of exact model knowledge. In a more realistic scenario with uncertain data and model mismatch, a feedback strategy that updates the policy weekly using model predictive control (MPC) leads to a reliable performance, even when applied to a validation model with deviant parameters. On top of that, we propose a robust MPC-based feedback policy using interval arithmetic that adapts the social distancing measures cautiously and safely, thus leading to a minimum number of fatalities even if measurements are inaccurate and the infection rates cannot be precisely specified by social distancing. Our theoretical findings support various recent studies by showing that (1) adaptive feedback strategies are required to reliably contain the COVID-19 outbreak, (2) well-designed policies can significantly reduce the number of fatalities compared to simpler ones while keeping the amount of social distancing measures on the same level, and (3) imposing stronger social distancing measures early on is more effective and cheaper in the long run than opening up too soon and restoring stricter measures at a later time.     

Generalized terminal state constraint for model predictive control

A terminal state equality constraint for Model Predictive Control (MPC) laws is investigated, where the terminal state/input pair is not fixed a priori but it is a free variable in the optimization. The approach, named “generalized” terminal state constraint, can be used for both tracking MPC (i.e. when the objective is to track a given steady state) and economic MPC (i.e. when the objective is to minimize a cost function which does not necessarily attains its minimum at a steady state). It is shown that the proposed technique provides, in general, a larger feasibility set with respect to the existing approaches, given the same prediction horizon. Moreover, a new receding horizon strategy is introduced, exploiting the generalized terminal state constraint. Under mild assumptions, the new strategy is guaranteed to converge in finite time, with arbitrarily good accuracy, to an MPC law with an optimally-chosen terminal state constraint, while still enjoying a larger feasibility set. The features of the new technique are illustrated by an inverted pendulum example in both the tracking and the economic contexts.     

Constrained stabilization via smooth Lyapunov functions

We consider the problem of stabilizing a dynamic system by means of bounded controls. We show that the largest domain of attraction can be arbitrarily closely approximated by a “smooth” domain of attraction for which we provide an analytic expression. Such an expression allows for the determination of a (non-linear) control law in explicit form.     

A multivariate adaptive regression B-spline algorithm (BMARS) for solving a class of nonlinear optimal feedback control problems

In this paper we present a novel method for solving a class of nonlinear optimal feedback control problems with moderately high dimensional state spaces, based on an adapted version of the BMARS algorithm. Numerical experiments were performed using problems with up to six state variables. The numerical results clearly demonstrate the efficiency and potential of the method for solving high dimensional problems.     

Evaluation and simple tuning of PID controllers with high-frequency robustness

An extensive study of robust and optimal tuning of PID controllers for stable non-oscillating plants is presented. It is built on a set of well defined criteria related to output performance, stability margins and control activity. Different interesting properties of the closed loop systems are observed. A set of simple tuning rules is based on these observations. These rules are compared to a couple of well established tuning methods and are shown to give well competitive results, especially when simplicity, low control activity and high-frequency robustness are emphasized. Derivative action is shown to improve performance significantly compared to PI control, with equal stability margin and a moderate increase of control activity, for most plants, including those with significant time delay.     

An automatic tuning methodology for a unified dead-time compensator

In this paper, an automatic tuning methodology for a modified Smith predictor control scheme is proposed. The main feature of the procedure is that it is applied in closed-loop (by either evaluating a set-point or a load disturbance step response) and it is suitable for self-regulating, integral and unstable processes. Further, the process parameter estimation technique is based on the evaluation of the integral of signals, thus making it inherently robust to measurement noise. Simulation and experimental results demonstrate the effectiveness of the methodology.     

Feedback spreading control laws for semilinear distributed parameter systems

The paper shows, for the first time that a feedback spreading control law for semilinear distributed parameter systems with compact linear operator can be provided by a selection procedure which involves both the dynamics of the system and the property to be spread. In the case of affine dependence upon the control a minimum energy feedback spreading control law will be derived by using a parametrized constrained optimization technique along with some facts of set-valued analysis.     

Optimal control problems with multiple characteristic time points in the objective and constraints

In this paper, we develop a computational method for a class of optimal control problems where the objective and constraint functionals depend on two or more discrete time points. These time points can be either fixed or variable. Using the control parametrization technique and a time scaling transformation, this type of optimal control problem is approximated by a sequence of approximate optimal parameter selection problems. Each of these approximate problems can be viewed as a finite dimensional optimization problem. New gradient formulae for the cost and constraint functions are derived. With these gradient formulae, standard gradient-based optimization methods can be applied to solve each approximate optimal parameter selection problem. For illustration, two numerical examples are solved.