Predictive switching supervisory control of persistently disturbed input-saturated plants

Predictive switching logic schemes are considered whereby a feedback-gain is switched-on at any time from a family of candidate feedback-gains so as to control a discrete-time input-saturated LTI system possibly subject to persistent bounded disturbances of unknown arbitrary magnitude. It is constructively shown that such schemes do exist which ensure, along with good tracking performance, global asymptotic and semi-global exponential stability in the noiseless case, as well as finite l_∞-induced gain to the disturbance-to-state map, whenever the structure of the disturbed plant can make such properties conceptually achievable, viz., the disturbance which enters an Asymptotically Null-Controllable with Bounded Input (ANCBI) system acts directly only on the stable modes, while the critically unstable ones are indirectly affected by the disturbance only via the feedback controls. More generally, in ANCBI systems general disturbances of suitably bounded magnitude can also be handled by the scheme, provided that the switching logic be equipped with an appropriate hysteresis facility.     

Affine and predictive control policies for a class of nonlinear systems

The input-state linear horizon (ISLH) for a nonlinear discrete-time system is defined as the smallest number of time steps it takes the system input to appear nonlinearly in the state variable. In this paper, we employ the latter concept and show that the class of constraint admissible N-step affine state-feedback policies is equivalent to the associated class of constraint admissible disturbance-feedback policies, provided that N is less than the system’s ISLH. The result generalizes a recent result in [Goulart, P. J., Kerrigan, E. C., Maciejowski, J. M. (2006). Optimization over state feedback policies for robust control with constraints. Automatica, 42(4), 523-533] and is significant because it enables one: (i) to determine a constraint admissible state-feedback policy by employing well-known convex optimization techniques; and (ii) to guarantee robust recursive feasibility of a class of model predictive control (MPC) policies by imposing a suitable terminal constraint. In particular, we propose an input-to-state stabilizing MPC policy for a class of nonlinear systems with bounded disturbance inputs and mixed polytopic constraints on the state and the control input. At each time step, the proposed MPC policy requires the solution of a single convex quadratic programme parameterized by the current system state.     

A neurofuzzy scheme to on-line identification in an adaptive–predictive control

A neurofuzzy scheme has been designed to carry out on-line identification, with the aim of being used in an adaptive–predictive dynamic matrix control (DMC) of unconstrained nonlinear systems represented by a transfer function with varying parameters. This scheme supplies to the DMC controller the linear model and the nonlinear output predictions at each sample instant, and is composed of two blocks. The first one makes use of a fuzzy partition of the external variable universe of discourse, which smoothly commutes between several linear models. In the second block, a recurrent linear neuron with interpretable weights performs the identification of the models by means of supervised learning. The resulting identifier has several main advantages: interpretability, learning speed, and robustness against catastrophic forgetting. The proposed controller has been tested both on simulation and on a real laboratory plant, showing a good performance.     

Nonlinear parametric predictive temperature control of a distillation column

The integration of a nonlinear reduced process model with Parametric Predictive Control (PPC) is discussed for the bottom temperature control of a stabilizer distillation column. One of the main objectives is ensure the quality of the bottom product despite disturbances and complex dynamics. The purpose is to balance nonlinear control with simplicity, facilitating implementation in a DCS. The controllers developed were first tested in a simulated environment and then in the field, showing good performance under a wide range of operating conditions. The use of an estimator to compensate for modeling errors and unmeasured disturbances is also discussed.     

Robust adaptive control of linearizable nonlinear single input systems with guaranteed error bounds

In this paper, a nonlinear robust adaptive control algorithm is designed and analyzed for a class of single-input nonlinear systems with unknown nonlinearities. The controller employs a single layer neural network to estimate the unknown plant nonlinearities on-line. The proposed controller is continuous and guarantees closed-loop semi-global stability and convergence of the tracking error to a small residual set. Furthermore, it handles the situation where the estimated plant becomes uncontrollable without any restrictive assumptions. In contrast to previous work on the same subject, the size of the residual tracking error can be specified a priori and is guaranteed by choosing certain design parameters. A procedure for choosing these parameters is presented. An example is used to demonstrate the performance and properties of the proposed scheme.     

Inherent robustness properties of quasi-infinite horizon nonlinear model predictive control

We consider inherent robustness properties of model predictive control (MPC) for continuous-time nonlinear systems with input constraints and terminal constraints. We show that MPC with a nominal prediction model and persistent but bounded disturbances has some degree of inherent robustness when the terminal control law and the terminal penalty matrix are chosen as the linear quadratic control law and the related Lyapunov matrix, respectively. We emphasize that the input constraint sets can be any compact set rather than convex sets, and our results do not depend on the continuity of the optimal cost function or of the control law in the interior of the feasible region.     

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.     

On stability of an input amplitude constrained predictive control system

This paper presents stability results for discrete-time model-based predictive control system subject to an input amplitude constraint. It is shown that the input amplitude constrained control system may provide a stable control system in the sense of BIBO when the system to be controlled is of a class of the system poles which consist of multiple integrators and a stable polynomial. The solution of Diophantine equations and their properties are addressed. Simulation study is also carried out and it is shown that the output of the system may converge to the reference signal for certain degree of constraints.     

A flight control system for aerial robots: algorithms and experiments

This paper presents a hierarchical flight control system for unmanned aerial vehicles. The proposed system executes high-level mission objectives by progressively substantiating them into machine-level commands. The acquired information from various sensors is propagated back to the higher layers for reactive decision making. Each vehicle is connected via standardized wireless communication protocol for scalable multi-agent coordination. The proposed system has been successfully implemented on a number of small helicopters and validated in various applications. Results from waypoint navigation, a probabilistic pursuit-evasion game and vision-based target tracking demonstrate the potential of the proposed approach toward intelligent flying robots.     

Stable redesign of predictive control

The paper deals with I/O versions of receding horizon controllers based on the minimization of multistep quadratic costs with the constraint that the terminal state goes to zero. The resulting control law yields stable closed-loop systems under sharp conditions. Simulation results are presented to both verify the theoretical analysis and relate the new control law with GPC     

Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations

Optimization problems in chemical engineering often involve complex systems of nonlinear DAE as the model equations. The direct multiple shooting method has been known for a while as a fast off-line method for optimization problems in ODE and later in DAE. Some factors crucial for its fast performance are briefly reviewed. The direct multiple shooting approach has been successfully adapted to the specific requirements of real-time optimization. Special strategies have been developed to effectively minimize the on-line computational effort, in which the progress of the optimization iterations is nested with the progress of the process. They use precalculated information as far as possible (e.g. Hessians, gradients and QP presolves for iterated reference trajectories) to minimize response time in case of perturbations. In typical real-time problems they have proven much faster than fast off-line strategies. Compared with an optimal feedback control computable upper bounds for the loss of optimality can be established that are small in practice. Numerical results for the Nonlinear Model Predictive Control (NMPC) of a high-purity distillation column subject to parameter disturbances are presented.     

Computationally efficient model predictive control for convection dominated parabolic systems

Convection–diffusion–reaction processes widely exist in chemical engineering and other sectors of industry. In many cases, these systems are convection-dominated and can be modelled by parabolic partial differential equations (PDEs) with a relatively dominant convection term. The control of these systems using traditional solution methods requires demanding computation to achieve high control performance. In this paper, a predictive control approach is developed for these systems using a new solution technique that combines the method of characteristics and finite difference approximation. The study shows that the proposed control approach is able to provide a computationally efficient control for convection-dominant parabolic systems.     

Adaptive neural network predictive control for nonlinear pure feedback systems with input delay

This paper presents an adaptive neural control design for nonlinear pure-feedback systems with an input time-delay. Novel state variables and the corresponding transform are introduced, such that the state-feedback control of a pure-feedback system can be viewed as the output-feedback control of a canonical system. An adaptive predictor incorporated with a high-order neural network (HONN) observer is proposed to obtain the future system states predictions, which are used in the control design to circumvent the input delay and nonlinearities. The proposed predictor, observer and controller are all online implemented without iterative predictive calculations, and the closed-loop system stability is guaranteed. The conventional backstepping design and analysis for pure-feedback systems are avoided, which renders the developed scheme simpler in its synthesis and application. Practical guidelines on the control implementation and the parameter design are provided. Simulation on a continuous stirred tank reactor (CSTR) and practical experiments on a three-tank liquid level process control system are included to verify the reliability and effectiveness.     

Robust constrained predictive control using comparison model

This paper proposes a quadratic programming (QP) approach to robust model predictive control (MPC) for constrained linear systems having both model uncertainties and bounded disturbances. To this end, we construct an additional comparison model for worst-case analysis based on a robust control Lyapunov function (RCLF) for the unconstrained system (not necessarily an RCLF in the presence of constraints). This comparison model enables us to transform the given robust MPC problem into a nominal one without uncertain terms. Based on a terminal constraint obtained from the comparison model, we derive a condition for initial states under which the ultimate boundedness of the closed loop is guaranteed without violating state and control constraints. Since this terminal condition is described by linear constraints, the control optimization can be reduced to a QP problem.     

蚁群算法滚动优化的LS-SVM预测控制研究

针对非线性过程预测控制的模型预测和滚动优化问题,提出一种蚁群算法滚动优化的最小二乘支持向量机(LS-SVM)新型预测控制器,该控制器以建模简单、精度高的LS-SVM作为预测模型,蚁群算法作为滚动优化策略,避免了滚动优化中复杂的梯度计算.仿真研究表明,该控制器具有良好的非线性控制效果.     

The long way toward multivariate predictive control of flotation processes

Flotation processes are very complex, and after more than one hundred years of history, there are few reports on applications of novel techniques in monitoring and control of flotation units, circuits and global plants. On the other hand, the successful application of multivariate predictive control on other processes is well known. In this paper, an analysis on how the characteristics of flotation processes, the quality of measurements of key variables, and the general lack of realistic dynamic models, are delaying the appropriate use of predictive control. In this context, the applications of multivariate statistics, such as PCA, to model the relationship between operating data for on-line diagnosis and fault detection and to build causal models are discussed. Also the use of PLS models to predict target variables for control purposes, is presented. Results, obtained at pilot and industrial scales, are discussed, introducing new ideas on how to obtain more valuable information from the usual available operating data of the plant, and particularly from froth images.     

On a generalized predictive control algorithm

Generalized predictive control algorithms with reference models on imputs and outputs of the process have been proposed recently in the literature. Thise algorithms are extended by introducing suitable weighting factors in the performance index and it is shown that such algorithms provide a combined feedback feedforward control resulting in pole-zero cancellation of poles which do not correspond to the reference model. Hence, the system behaves asymptotically as the reference model provided the cancelled poles are stable. Therefore, a careful analysis of the stability of those poles in still needed.     

On improvement of transient performance in tracking control for a class of nonlinear systems with input saturation

This paper studies the technique of the composite nonlinear feedback (CNF) control for a class of cascade nonlinear systems with input saturation. The objective of this paper is to improve the transient performance of the closed-loop system by designing a CNF control law such that the output of the system tracks a step input rapidly with small overshoot and at the same time maintains the stability of the whole cascade system. The CNF control law consists of a linear feedback control law and a nonlinear feedback control law. The linear feedback law is designed to yield a closed-loop system with a small damping ratio for a quick response, while the nonlinear feedback law is used to increase the damping ratio of the closed-loop system when the system output approaches the target reference to reduce the overshoot. The result has been successfully demonstrated by numerical and application examples including a flight control system for a fighter aircraft.     

Explicit/multi-parametric model predictive control (MPC) of linear discrete-time systems by dynamic and multi-parametric programming

This work presents a new algorithm for solving the explicit/multi-parametric model predictive control (or mp-MPC) problem for linear, time-invariant discrete-time systems, based on dynamic programming and multi-parametric programming techniques. The algorithm features two key steps: (i) a dynamic programming step, in which the mp-MPC problem is decomposed into a set of smaller subproblems in which only the current control, state variables, and constraints are considered, and (ii) a multi-parametric programming step, in which each subproblem is solved as a convex multi-parametric programming problem, to derive the control variables as an explicit function of the states. The key feature of the proposed method is that it overcomes potential limitations of previous methods for solving multi-parametric programming problems with dynamic programming, such as the need for global optimization for each subproblem of the dynamic programming step.     

数字式预见控制的计算机算法研究

分析了计算机实现数字式预见控制的主要问题,给出了一种Riccati方程式的数字解法,提出了用计算机实现数字式预见控制的可行性和算法。研究表明这种算法的精度较高,易于计算机实现。