Convergence in economic model predictive control with average constraints

In this paper, we thoroughly investigate various aspects of economic model predictive control with average constraints, i.e., constraints on average values of state and input variables. In particular, we first show that a certain time-varying output constraint has to be included into the MPC problem formulation in order to ensure fulfillment of these average constraints. Optimizing a general (possibly economic) performance criterion may result in a non-converging behavior of the corresponding closed-loop system. While such a behavior might be acceptable in some cases, it may be undesirable for other types of applications. Hence as a second contribution, we provide a Lyapunov-like analysis to conclude that indeed asymptotic convergence to the optimal steady-state follows if the system satisfies a certain dissipativity condition. Finally, for the case that this dissipativity property is not satisfied but still a convergent behavior of the closed-loop is required, we examine two different methods how convergence can be enforced within an economic MPC setup by imposing additional average constraints on the system. In the first method, an additional average constraint is defined which results in the system being dissipative, while the second consists of imposing an additional even zero-moment average constraint. We illustrate our results with various examples.     

MPC for tracking piecewise constant references for constrained linear systems

In this paper, a novel model predictive control (MPC) for constrained (non-square) linear systems to track piecewise constant references is presented. This controller ensures constraint satisfaction and asymptotic evolution of the system to any target which is an admissible steady-state. Therefore, any sequence of piecewise admissible setpoints can be tracked without error. If the target steady state is not admissible, the controller steers the system to the closest admissible steady state.These objectives are achieved by: (i) adding an artificial steady state and input as decision variables, (ii) using a modified cost function to penalize the distance from the artificial to the target steady state (iii) considering an extended terminal constraint based on the notion of invariant set for tracking. The control law is derived from the solution of a single quadratic programming problem which is feasible for any target. Furthermore, the proposed controller provides a larger domain of attraction (for a given control horizon) than the standard MPC and can be explicitly computed by means of multiparametric programming tools. On the other hand, the extra degrees of freedom added to the MPC may cause a loss of optimality that can be arbitrarily reduced by an appropriate weighting of the offset cost term.     

Direct adaptive fuzzy control of nonlinear strict-feedback systems

This paper focuses on adaptive fuzzy tracking control for a class of uncertain single-input /single-output nonlinear strict-feedback systems. Fuzzy logic systems are directly used to approximate unknown and desired control signals and a novel direct adaptive fuzzy tracking controller is constructed via backstepping. The proposed adaptive fuzzy controller guarantees that the output of the closed-loop system converges to a small neighborhood of the reference signal and all the signals in the closed-loop system remain bounded. A main advantage of the proposed controller is that it contains only one adaptive parameter that needs to be updated online. Finally, an example is used to show the effectiveness of the proposed approach.     

A multivariable MRAC scheme with application to a nonlinear aircraft model

This paper revisits the multivariable model reference adaptive control (MRAC) problem, by studying adaptive state feedback control for output tracking of multi-input multi-output (MIMO) systems. With such a control scheme, the plant-model matching conditions are much less restrictive than those for state tracking, while the controller has a simpler structure than that of an output feedback design. Such a control scheme is useful when the plant-model matching conditions for state tracking cannot be satisfied. A stable adaptive control scheme is developed based on LDS decomposition of the high-frequency gain matrix, which ensures closed-loop stability and asymptotic output tracking. A simulation study of a linearized lateral-directional dynamics model of a realistic nonlinear aircraft system model is conducted to demonstrate the scheme. This linear design based MRAC scheme is subsequently applied to a nonlinear aircraft system, and the results indicate that this linearization-based adaptive scheme can provide acceptable system performance for the nonlinear systems in a neighborhood of an operating point.     

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.     

Adaptive local tracking of a temperature profile in tubular reactor with partial measurements

In this work, a local constrained adaptive output feedback is presented for a class of exothermic tubular reactors models described by a nonlinear partial differential equations. The considered output is the measured temperature in a fixed zone of the reactor to regulate the temperature throughout the reactor to a ball with radius λ (arbitrarily small) centered at the fixed temperature profile. For a given measurement zone with length given in terms of the desired profile and λ and for initial temperature in a fixed domain, it is shown that the tracking error through the reactor tends asymptotically to a ball of arbitrary prescribed radius λ > 0, centered at the given temperature profile. Numerical simulations have been performed to illustrate the performance of the proposed approach.     

低速行驶重型车辆的动力学系统建模与非线性控制

考虑低速行驶工况下的重型车辆,本文建立其纵向行驶驱/制动系统的非线性动力学方程. 在此基础上采用反馈线性化方法将驱/制动工况下的非线性系统转化为线性可控正则型,并针对制动工况下非线性系统存在的控制时滞,提出一种基于非线性SMITH 预估方法的反馈线性化变换,该变换在有效补偿控制时滞同时,实现了制动系统的线性可控正则型转换. 最后,分别基于驱/制动系统的线性可控正则型设计跟踪控制器,实现了车辆低速工况的加/减速度精确跟踪控制.     

一类非线性系统的直接自适应控制器

针对带一类非线性参数系统的状态反馈自适应跟踪控制问题,通过设计一种新的李亚普诺夫函数--加权控制李亚普诺夫函数,由它作用于控制器和参数调整律,使之达到全局渐近跟踪从而满足控制指标。     

Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints

In this paper, adaptive tracking control is proposed for a class of uncertain multi-input and multi-output nonlinear systems with non-symmetric input constraints. The auxiliary design system is introduced to analyze the effect of input constraints, and its states are used to adaptive tracking control design. The spectral radius of the control coefficient matrix is used to relax the nonsingular assumption of the control coefficient matrix. Subsequently, the constrained adaptive control is presented, where command filters are adopted to implement the emulate of actuator physical constraints on the control law and virtual control laws and avoid the tedious analytic computations of time derivatives of virtual control laws in the backstepping procedure. Under the proposed control techniques, the closed-loop semi-global uniformly ultimate bounded stability is achieved via Lyapunov synthesis. Finally, simulation studies are presented to illustrate the effectiveness of the proposed adaptive tracking control.     

控制方向未知的非线性系统的自适应输出跟踪控制

针对一类含有未知控制方向和时变不确定性的本质非线性系统,应用Nussbaum-type增益技术和Adding a power integrator递推设计方法,设计了一种鲁棒自适应状态反馈拉制器．所设计的控制器能保证闭环系统所有信号全局一致有界,特别是通过适当调整控制器设计参数,可使输出跟踪误差在有限时间后变得适当小．最后通过仿真实例对算法进行验证.