Real-time design of an adaptive nonlinear predictive controller

Based on real-time identification and using the concept of NARX (Nonlinear AutoRegressive with exogenous inputs) models, a new adaptive nonlinear predictive controller (ANPC) design is proposed. NARX models represent a natural way to describe the input-output relationship of severely nonlinear systems. From an initial batch of input-output data, a parsimonious NARX model is obtained using the Modified Gram-Schmidt (MGS) orthogonalization algorithm. Following this initial off-line identification and model reduction procedure, the control loop is closed. The ANPC directly uses the obtained structure and initial parameter estimates, which are updated each time step using recursive identification. The controller is designed similar to a typical linear predictive controller based on solving a nonlinear programming (NLP) problem. This paper shows how to solve this NLP problem on-line without the knowledge of the NARX model structure. The design is given for the multi-input multi-output (MIMO) case.     

Adaptive air-fuel ratio control with MLP network

This paper presents an application of adaptive neural network model-based predictive control (MPC) to the air-fuel ratio of an engine simulation. A multi-layer perceptron (MLP) neural network is trained using two on-line training algorithms: a back propagation algorithm and a recursive least squares (RLS) algorithm. It is used to model parameter uncertainties in the nonlinear dynamics of internal combustion (IC) engines. Based on the adaptive model, an MPC strategy for controlling air-fuel ratio is realized, and its control performance compared with that of a traditional PI controller. A reduced Hessian method, a newly developed sequential quadratic programming (SQP) method for solving nonlinear programming (NLP) problems, is implemented to speed up nonlinear optimization in the MPC.     

Stabilizing low complexity feedback control of constrained piecewise affine systems

Piecewise affine (PWA) systems are powerful models for describing both non-linear and hybrid systems. One of the key problems in controlling these systems is the inherent computational complexity of controller synthesis and analysis, especially if constraints on states and inputs are present. In addition, few results are available which address the issue of computing stabilizing controllers for PWA systems without placing constraints on the location of the origin.This paper first introduces a method to obtain stability guarantees for receding horizon control of discrete-time PWA systems. Based on this result, two algorithms which provide low complexity state feedback controllers are introduced. Specifically, we demonstrate how multi-parametric programming can be used to obtain minimum-time controllers, i.e., controllers which drive the state into a pre-specified target set in minimum time. In a second segment, we show how controllers of even lower complexity can be obtained by separately dealing with constraint satisfaction and stability properties. To this end, we introduce a method to compute PWA Lyapunov functions for discrete-time PWA systems via linear programming. Finally, we report results of an extensive case study which justify our claims of complexity reduction.     

一种高效的快速近似控制向量参数化方法

控制向量参数化(Control vector parameterization, CVP) 方法是目前求解流程工业中最优操作问题的主流数值方法,然而,该方法的主要缺点之一是 计算效率较低,这是因为在求解生成的非线性规划(Nonlinear programming, NLP) 问题时,需要随着控制参数的调整,反复不断地求解相关的微分方程组,这也是CVP 方法中最耗时的部分.为了提高CVP 方法的计算效率,本文提出一种新颖的快速近似方法,能够有效减少微分方程组、函数值以及 梯度的计算量.最后,两个经典的最优控制问题上的测试结果及与国外成熟的最优控制 软件的比较研究表明:本文提出的快速近似CVP 方法在精度和效率上兼有良好的表现.     

Adaptive neuro-genetic control of chaos applied to the attitude control problem

Conventional adaptive control techniques have, for the most part, been based on methods for linear or weakly non-linear systems. More recently, neural network and genetic algorithm controllers have started to be applied to complex, non-linear dynamic systems. The control of chaotic dynamic systems poses a series of especially challenging problems. In this paper, an adaptive control architecture using neural networks and genetic algorithms is applied to a complex, highly nonlinear, chaotic dynamic system: the adaptive attitude control problem (for a satellite), in the presence of large, external forces (which left to themselves led the system into a chaotic motion). In contrast to the OGY method, which uses small control adjustments to stabilize a chaotic system in an otherwise unstable but natural periodic orbit of the system, the neuro-genetic controller may use large control adjustments and proves capable of effectively attaining any specified system state, with no a prioriknowledge of the dynamics, even in the presence of significant noise.This work was partly supported by SERC grant 90800355.     

Optimization method for solving bang-bang and singular control problems

In this paper we study optimal control problems with the control variable appearing linearly.A novel method for optimization with respect to the switching times of controls containing both bang-bang and singular arcs is presented.This method transforms the control problem into a finite-dimensional optimization problem by reformulating the control problem as a multi-stage optimization problem.The optimal control problem is partitioned as several stages, with each stage corresponding to a particular control arc.A control vector parameterization approach is applied to convert the control problem to a static nonlinear programming(NLP) problem.The control profiles and stage lengths act as decision variables.Based on the Pontryagin maximal principle,a multi-stage adjoint system is constructed to calculate the gradients required by the NLP solvers.Two examples are studied to demonstrate the effectiveness of this strategy.     

Partially observed non-linear risk-sensitive optimal stopping control for non-linear discrete-time systems

In this paper we introduce and solve the partially observed optimal stopping non-linear risk-sensitive stochastic control problem for discrete-time non-linear systems. The presented results are closely related to previous results for finite horizon partially observed risk-sensitive stochastic control problem. An information state approach is used and a new (three-way) separation principle established that leads to a forward dynamic programming equation and a backward dynamic programming inequality equation (both infinite dimensional). A verification theorem is given that establishes the optimal control and optimal stopping time. The risk-neutral optimal stopping stochastic control problem is also discussed.     

Advanced-multi-step nonlinear model predictive control

Nonlinear model predictive control (NMPC) has gained widespread attention due to its ability to handle variable bounds and deal with multi-input, multi-output systems. However, it is susceptible to computational delay, especially when the solution time of the nonlinear programming (NLP) problem exceeds the sampling time. In this paper we propose a fast NMPC method based on NLP sensitivity, called advanced-multi-step NMPC (amsNMPC). Two variants of this method are developed, the parallel approach and the serial approach. For the amsNMPC method, NLP problems are solved in background multiple sampling times in advance, and manipulated variables are updated on-line when the actual states are available. We present case studies about a continuous stirred tank reactor (CSTR) and a distillation column to show the performance of amsNMPC. Nominal stability properties are also analyzed.     

Improving vehicle performance using adaptive control techniques

This paper reviews a collaborative research programme aimed at improving vehicle performance using adaptive control techniques. Initially the design of active suspension systems is considered, and the benefits of using a non-linear controller model with an adaptive control scheme are discussed. Adaptive schemes for active roll control are then considered, and the merits of incorporating a Smith predictor to accommodate for system delays are high-lighted. Preliminary research in adaptive cruise control and collision avoidance is discussed and plans for further developments are outlined. This work was presented, in part, at the Third International Symposium on Artificial Life and Robotics, Oita, Japan, 19–21 January 1998     

Robust and adaptive control: fidelity or an open relationship?

Robust and adaptive control are essentially meant to solve the same control problem. Given an uncertain LTI model set with the assumption that the controlled plant slowly drifts or occasionally jumps in the allowed model set, find a controller that satisfies the given servo and disturbance rejection specifications. Specifications on the transient response to a sudden plant change or “plant jump” are easily incorporated into the robust control problem, and if a solution is found, the robust control system does indeed exhibit satisfactory transients to plant jumps. The reason to use adaptive control is its ability, when the plant does not jump, to maintain the given specifications with a lower-gain control action (or to achieve tighter specifications), and also to solve the control problem for a larger uncertainty set than a robust controller. Certainly equivalence-based adaptive controllers, however, often exhibit insufficient robustness and unsatisfactory transients to plant jumps. It is therefore suggested in this paper that adaptive control always be built on top of a robust controller in order to marry the advantages of robust and adaptive control. The concept is called adaptive robust control. It may be compared with gain scheduling, two-time scale adaptive control, intermittent adaptive control, repeated auto-tuning, or switched adaptive control, with the important difference that the control is switched between robust controllers that are based on plant uncertainty sets that take into account not only the currently estimated plant model set but also the possible jumps and drifts that may occur until the earliest next time the controller can be updated.     

时变不确定性系统的二自由度最优鲁棒稳态跟踪控制器设计

研究了被控系统存在范数有界的时变模型摄动和未知外部干扰时鲁棒稳态跟踪问题. 利用二自由度控制结构和Youla参数化方法.提出了一个最坏情况稳态绝对误差的精确计算公 式,利用该公式最优稳态跟踪控制器设计问题可化为一个有限维l1优化问题.因此控制器设计 只需解一个标准线性规划问题.此外,还证明了所提出的控制器可同时保证系统的鲁棒稳定性 和最优跟踪性能.仿真结果表明了该方法的有效性和可行性.     

Probabilistic dual heuristic programming-based adaptive critic

Adaptive critic (AC) methods have common roots as generalisations of dynamic programming for neural reinforcement learning approaches. Since they approximate the dynamic programming solutions, they are potentially suitable for learning in noisy, non-linear and non-stationary environments. In this study, a novel probabilistic dual heuristic programming (DHP)-based AC controller is proposed. Distinct to current approaches, the proposed probabilistic (DHP) AC method takes uncertainties of forward model and inverse controller into consideration. Therefore, it is suitable for deterministic and stochastic control problems characterised by functional uncertainty. Theoretical development of the proposed method is validated by analytically evaluating the correct value of the cost function which satisfies the Bellman equation in a linear quadratic control problem. The target value of the probabilistic critic network is then calculated and shown to be equal to the analytically derived correct value. Full derivation of the Riccati solution for this non-standard stochastic linear quadratic control problem is also provided. Moreover, the performance of the proposed probabilistic controller is demonstrated on linear and non-linear control examples.     

最优控制问题的Legendre 伪谱法求解及其应用

伪谱法通过全局插值多项式参数化状态和控制变量,将最优控制问题(OCP)转化为非线性规划问题(NLP)进行求解,是一类具有更高求解效率的直接法。总结Legendre伪谱法转化Bolza型最优控制问题的基本框架,推导OCP伴随变量与NLP问题KKT乘子的映射关系,建立基于拟牛顿法的LGL配点数值计算方法,并针对非光滑系统,进一步研究分段伪谱逼近策略。基于上述理论开发通用OCP求解器,并对3个典型最优控制问题进行求解,结果表明了所提出方法和求解器的有效性。     

Globally optimal nonlinear model predictive control based on multi-parametric disaggregation

Nonlinear model predictive control is appropriate for controlling highly nonlinear processes, particularly when operating conditions change frequently. If the problem is nonconvex, the controller must lead the process to a global, rather than a local optimum. This work deals with computation of the control actions which lead to the global optimum via the normalized multi-parametric disaggregation technique. The continuous process model is transformed into a nonlinear programming (NLP) problem via discretization which uses an implicit integration method. The NLP problem is relaxed into a mixed integer linear programming (MILP) model. Iterations between solving MILP (lower bound) and using its solution as a starting point for a local nonlinear optimizer (which computes the upper bound) continue until the gap is closed (an l₁-norm objective function is used). Controller performance is illustrated by several examples. Relative simplicity of the algorithm makes it possible to be implemented by a wide audience.     

Adaptive Controller Design for Unknown Systems Using Measured Data

This paper presents a measurement‐based adaptive control design approach for unknown systems working over a wide range of operating conditions. Traditional control design approaches usually require the availability of a mathematical model. However, it has been shown in many practical situations that, due to complex dynamics of physical systems, some simplifying assumptions are made for the derivation of mathematical models. Hence, controller design based on simplified models may result in degradation of the desired closed‐loop performance. Data‐based control design approaches can be viewed as an alternative approach to model‐based methods. Most data‐based control methods available in the literature aim to design controllers for unknown systems that operate only at a given operating point. However, the dynamical behavior of plants may change for different operating conditions, which makes the task of designing a controller that works over the entire range of operating conditions more challenging. In this paper, we address such a problem and propose to design adaptive controllers based on measured data. Such a proposed method is based on designing a set of measurement‐based controllers validated at a finite set of pre‐specified operating points. Then, the parameters of the adaptive controller are obtained by interpolating between the set of pre‐designed controller parameters to derive a gain‐scheduling controller. Moreover, low‐order adaptive controllers can be designed by simply selecting the desired controller structure. The efficacy of the proposed approach is experimentally validated through a practical application to control a heating system operated over a large range of flow rate.     

基于腿部关节控制的仿人机器人偏摆力矩控制方法

针对机器人步行过程中产生的偏摆力矩影响步行稳定性的问题, 提出一种全新的基于腿部关节控制的偏摆力矩控制方法. 分析了偏摆力矩产生的原因及步行过程中垂直方向上的力矩平衡条件; 根据仿人机器人连杆模型和力矩平衡条件, 将偏摆力矩控制问题转化为带约束条件的二次规划问题, 推导出支撑腿腿部关节角度控制的表达式, 设计了腿部关节自适应控制器以提高轨迹跟踪性能, 并给出了稳定性证明. 仿真结果表明, 该方法能较好地克服偏摆力矩的影响, 使机器人实现稳定的步行.

     

A Priori Open Loop Optimal Control of Continuous Time Stochastic Systems†

This paper is presented, not so much as an end in itself concerning the solution of a definite engineering problem, but as an exploratory step toward the solution of the problem of optimal control of continuous time stochastic non-linear systems when only noisy observations of the state are available. In this paper, the problem of determining the optimal open loop control, when no observations at all are available, is treated by dynamic programming. The main results of the paper are to obtain the functional equation of dynamic programming and to present a quasi-linearization type of algorithm for its solution. The author's intention was to illustrate by these results that infinite dimensional function space is the most natural setting for stochastic non-linear problems. The results obtained give some insight into what can be expected in the more general case of noisy observations. In the Appendices an argument is presented to justify the proposed algorithm and an example is given for which an exact solution to the functional equation of dynamic programming can be obtained.     

Model based approach to closed loop control of 1-D engine simulation models

1-D engine simulation models are widely used for the analysis and verification of air-path design concepts to assess performance and therefore determine suitable hardware. The transient response is a key driver in the selection process which in most cases requires closed loop control of the model to ensure operation within prescribed physical limits and tracking of reference signals. Since the controller effects the system performance a systematic procedure which achieves close-to-optimal performance is desired, if the full potential of a given hardware configuration is to be properly assessed. For this purpose a particular implementation of Model Predictive Control (MPC) based on a corresponding Mean Value Engine Model (MVEM) is reported here. The MVEM is linearised on-line at each operating point to allow for the formulation of quadratic programming (QP) problems, which are solved as the part of the proposed MPC algorithm. The MPC output is used to control a 1-D engine model. The closed loop performance of such a system is benchmarked against the solution of a related optimal control problem (OCP). The system is also tested for operation at high altitude conditions to demonstrate the ability of the controller to respect specified physical constraints. As an example this study is focused on the transient response of a light-duty automotive Diesel engine. For the cases examined the proposed controller design gives a more systematic procedure than other ad hoc approaches that require considerable tuning effort.     

Optimal genetic manipulations in batch bioreactor control

Advances in metabolic engineering have enabled bioprocess optimization at the genetic level. Large-scale systematic models are now available at a genome level for many biological processes. There is, thus, a motivation to develop advanced control algorithms, using these complex models, to identify optimal performance strategies both at the genetic and bioreactor level. In the present paper, the bilevel optimization framework previously developed by the authors is coupled with control algorithms to determine the genetic manipulation strategies in practical bioprocess applications. The bilevel optimization includes a linear programming problem in the inner level and a nonlinear optimization problem in the outer level. Both gradient-based and stochastic methods are used to solve the nonlinear optimization problem. Ethanol production in an anaerobic batch fermentation of Escherichia coli is considered in case studies that demonstrate optimization of ethanol production, batch time, and multi-batch scheduling.     

CG伪谱法在欠驱动航天器姿态机动最优控制中的应用

使用Chebyshev-Gauss(CG)伪谱法研究带动量轮和推力器的欠驱动航天器姿态最优控制问题.基于欧拉姿态角和动量矩定理导出两类航天器姿态运动模型,采用Clenshaw-Curtis积分近似得到性能指标函数中的积分项,应用重心拉格朗日插值逼近状态变量和控制变量,将连续最优控制问题离散为具有代数约束的非线性规划(NLP)问题,通过序列二次规划(SQP)算法求解.数值仿真结果表明,对两类欠驱动航天器的姿态机动最优控制均能达到设计控制要求,得到的姿态最优曲线与验证得到的曲线几乎完全重叠.