Optimal realizations of fixed-point implemented digital controllers with the smallest dynamic range

A novel approach is proposed to design optimal finite word length (FWL) realizations of digital controllers implemented in fixed-point arithmetic. A minimax-based search procedure is first formulated to obtain an optimal controller realization that optimizes an FWL closed-loop stability measure. Since this FWL closed-loop stability measure is solely linked to the fractional part or precision of fixed-point format, the resulting realization may not have the smallest dynamic range. A measure is then derived to indicate the dynamic range of fixed-point implemented realization. By choosing an appropriate orthogonal transformation of this dynamic range measure of the optimal precision controller realization, a numerical optimization method is developed to make the controller realization having the smallest dynamic range without sacrificing FWL closed-loop stability robustness. The proposed approach is more efficient than a direct optimization of some combined FWL closed-loop stability and dynamic range measure via a numerical means. The proposed approach is established within a unified framework that includes both the shift and delta operator parameterizations, which makes it possible to compare the closed-loop stability characteristics of the optimal FWL controller realizations using shift and delta operators, respectively. Through analysing the simulation results of a design example, some useful insights and understandings are obtained regarding the FWL controller realizations based on shift and delta operators.     

Comparative study on optimizing closed-loop stability bounds of finite-precision controller structures with shift and delta operators

The paper analyzes the sensitivity of closed-loop stability with respect to (w.r.t.) finite word length (FWL) effects in the implementation of the controller coefficients using both the shift and delta operator parameterizations. A unified approach is established to optimize a closed-loop stability lower bound for FWL controller structures. This provides a general framework to compare the FWL closed-loop stability characteristics of the controller structures based on the shift and delta operators, respectively. Two numerical examples are given, and the simulation results show that the optimal FWL controller realizations with the delta operator have better closed-loop stability margins than those with the shift operator.     

Real‐time model predictive control based on dual gradient projection: Theory and fixed‐point FPGA implementation

This paper proposes a method to design robust model predictive control (MPC) laws for discrete‐time linear systems with hard mixed constraints on states and inputs, in case of only an inexact solution of the associated quadratic program is available, because of real‐time requirements. By using a recently proposed dual gradient‐projection algorithm, it is proved that the discrepancy of the optimal control law as compared with the obtained one is bounded even if the solver is implemented in fixed‐point arithmetic. By defining an alternative MPC problem with tightened constraints, a feasible solution is obtained for the original MPC problem, which guarantees recursive feasibility and asymptotic stability of the closed‐loop system with respect to a set including the origin, also considering the presence of external disturbances. The proposed MPC law is implemented on a field‐programmable gate array in order to show the practical applicability of the method. Copyright © 2016 John Wiley & Sons, Ltd.     

Sliding mode fault‐tolerant control of uncertain system: A delta operator approach

This paper is concerned with the sliding mode control of uncertain nonlinear systems against actuator faults and external disturbances based on delta operator approach. The nonlinearity, actuator fault, and external disturbance are considered in this study, and the bounds of Euclidean norms of the nonlinearity and the specific lower and upper bounds of the actuator faults and the disturbances are unknown knowledge. Our attention is mainly focused on designing a sliding mode fault‐tolerant controller to compensate the effects from the nonlinearity, unknown actuator fault, and external disturbance. Based on Lyapunov stability theory, a novel‐adaptive fault‐tolerant sliding mode control law is deigned such that the resulting closed loop delta operator system is finite‐time convergence and the actuator faults can be tolerated, simultaneously. Finally, simulation results are provided to verify the effectiveness of the proposed control design scheme. Copyright © 2017 John Wiley & Sons, Ltd.     

Insensitive output feedback H ∞ control of delta operator systems with insensitivity to sampling time jitter

The insensitive multi‐objective H _∞ control synthesis problem via dynamic output feedback for linear delta operator systems with insensitivity to sampling time jitter is investigated in the case of small sampling times. The delta‐domain model instead of the standard shift‐domain model is used to avoid the inherent numerical ill‐condition resulting from using the latter model at high sampling rates. Parameter sensitivity function of the transfer function with respect to sampling time is defined to mitigate the effect of sampling time jitter because it may cause significant degradation of the overall system performance. It is worth pointing out that a novel bounded real lemma for delta operator allowing extra degree of freedom for multi‐objective control design is presented by using the well‐known projection lemma. Then, from this new lemma, a two‐step design procedure based on LMI is presented to design insensitive dynamic output feedback controllers such that the resulting closed‐loop system is asymptotically stable and meets the requirement of sensitivity specification. A numerical example is also presented to show the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Transient performance for discrete‐time singular systems with actuators saturation via composite nonlinear feedback control

This paper is concerned with the transient performance improvement in tracking control problems for linear multivariable discrete‐time singular systems subject to actuators saturation. A composite nonlinear feedback control strategy is considered, and the resulting controller consists of a linear feedback law and a nonlinear feedback law without any switching element. The nonlinear term leads to a varying damping ratio of the closed‐loop system and yields a small overshoot as the output approaches the target reference, whereas the linear component is designed to achieve a quick response of the closed‐loop system. Two composite nonlinear feedback control laws by both state feedback and measurement output feedback are addressed. An illustrative example is included to show the validity of the obtained results. Copyright © 2012 John Wiley & Sons, Ltd.     

Quantized stabilization of networked control systems with actuator saturation

In this paper, we investigate the problems of stabilization of networked control systems with quantization and actuator saturation via delta operator approach. The definition of the domain of attraction for delta operator systems is introduced to analyze the stochastic stability of the closed‐loop networked control systems. The quantizer is a uniform one with arbitrary quantization regions, and the packet dropout process is modeled as a Bernoulli process. On the basis of the zoom strategy and Lyapunov theory in delta domain, sufficient conditions are given for the closed‐loop delta operator systems to be mean square stable, and the feedback controllers are designed to ensure the stability of networked control systems. A single link direct joint driven manipulator model is presented to show the effectiveness of the main results. Copyright © 2016 John Wiley & Sons, Ltd.     

Stabilization of networked control systems with nonuniform random sampling periods

In this paper, a new linear delayed delta operator switched system model is proposed to describe networked control systems with packets dropout and network‐induced delays. The plant is a continuous‐time system, which is sampled by time‐varying random sampling periods. A general delta domain Lyapunov stability criterion is given for delta operator switched systems with time delays. Sufficient conditions for asymptotic stability of closed‐loop networked control systems with both packets dropout and network‐induced delays are presented in terms of linear matrix inequalities (LMIs). A verification theorem is given to show the solvability of the stabilization conditions by solving a class of finite LMIs. Both the case of data packets arrive instantly and the case of invariant sampling periods in delta operator systems are given, respectively. Three numerical examples are given to illustrate the effectiveness and potential of the developed techniques. Copyright © 2010 John Wiley & Sons, Ltd.     

Digital Redesign Of Continuous‐Time Suboptimal Tracker For Two‐Dimensional Systems

In this paper, the digital redesign of a continuous suboptimal tracker for the two‐dimensional (2‐D) systems is proposed. This paper presents a new optimal digital redesign technique of 2‐D systems for finding a dynamic digital control law from the given continuous‐time 2‐D systems by minimizing a quadratic cost function (performance index). We directly convert the original continuous‐time 2‐D quadratic cost function into the discretized form and solve the optimization problem in the discrete‐time domain. The developed optimal digital redesign control law enables the output of the digitally controlled closed‐loop systems to closely match the reference signal for 2‐D systems, and it can be easily implemented using microcomputers. An illustrative example is presented to demonstrate the effectiveness of the proposed procedure.     

Global stabilization of discrete‐time feedforward time‐delay systems by bounded controls

This paper studies the problem of global stabilization of a family of discrete‐time feedforward time‐delay systems with bounded controls. Two classes of nonlinear control laws are established based on a special canonical form of the considered system. The proposed control laws use not only the current states but also the delayed states for feedback and, moreover, contain some free parameters. These advantages can help to improve the transient performance of the closed‐loop system significantly. A practical example is given for illustration.     

Robust Constrained Model Predictive Control for Discrete‐Time Uncertain System in Takagi‐Sugeno's Form

In this paper, we investigate a robust constrained model predictive control synthesis approach for discrete‐time Takagi‐Sugeno's (T‐S) fuzzy system with structured uncertainty. The key idea is to determine, at each sampling time, a state feedback fuzzy predictive controller that minimizes the performance objective function in the infinite time horizon by solving a class of linear matrix inequalities (LMIs) optimization problem. To do this, the fuzzy predictive controller is designed on the basis of non‐parallel distributed compensation (non‐PDC) control law, relaxed stability conditions of the closed‐loop fuzzy system are developed by employing an extended nonquadratic Lyapunov function and introducing additional slack and collection matrices. In addition, the presented approach is capable of ensuring the robust asymptotic stability as well as the recursive feasibility of the closed‐loop fuzzy system. Simulations on a highly nonlinear continuous stirred tank reactor (CSTR) are eventually presented to demonstrate the effectiveness of the developed theoretical approach.     

Pseudo‐predictor feedback control of discrete‐time linear systems with a single input delay

This paper studies the problems of stabilization of discrete‐time linear systems with a single input delay. By developing the methodology of pseudo‐predictor feedback, which uses the (artificial) closed‐loop system dynamics to predict the future state, memoryless state feedback control laws are constructed to solve the problem. Necessary and sufficient conditions are obtained to guarantee the stability of the closed‐loop system in terms of the stability of a class‐difference equations. It is also shown that the proposed controller achieves semi‐global stabilization of the system if its actuator is subject to either magnitude saturation or energy constraints under the condition that the open‐loop system is only polynomially unstable. Numerical examples have been worked out to illustrate the effectiveness of the proposed approaches. Copyright © 2015 John Wiley & Sons, Ltd.     

Stability of a Trajectory‐Based Control Law for an Unknown Nonlinear Non‐Minimum Phase System

We investigate the stability of an unknown nonlinear discrete‐time non‐minimum phase system under a trajectory‐based control law. The system can be regarded as a first‐order approximation to a continuous‐time system. Hence, one of the parameters in the discrete‐time system equation can be regarded as the “sampling interval”. We show that, subject to certain conditions, as long as the sampling interval is neither too short nor too long, the closed‐loop system is stable in a certain sense.     

A -based optimal finite-word-length controller design

A novel optimal Finite Word Length (FWL) controller design is proposed in the framework of μ theory. A computationally tractable close-loop stability measure with FWL implementation considerations of the controller is derived based on the μ theory, and the optimal FWL controller realizations are obtained by solving the resulting optimal FWL realization problem using linear matrix inequality techniques.     

Optimal fixed‐structure control for linear non‐negative dynamical systems

In this paper, we develop optimal output feedback controllers for set‐point regulation of linear non‐negative dynamical systems. Specifically, using a constrained fixed‐structure control framework we develop optimal output feedback control laws that guarantee that the trajectories of the closed‐loop system remain in the non‐negative orthant of the state space for non‐negative initial conditions. In addition, we characterize domains of attraction predicated on closed and open Lyapunov level surfaces contained in the non‐negative orthant for unconstrained optimal linear‐quadratic output feedback controllers. Output feedback controllers for compartmental systems with non‐negative inputs are also given. Copyright © 2004 John Wiley & Sons, Ltd.     

Optimal robot‐environment interaction using inverse differential Riccati equation

An optimal robot‐environment interaction is designed by transforming an environment model into an optimal control problem. In the optimal control, the inverse differential Riccati equation is introduced as a fixed‐end‐point closed‐loop optimal control over a specific time interval. Then, the environment model, including interaction force, is formulated in a state equation, and the optimal trajectory is determined by minimizing a cost function. Position control is proposed, and the stability of the closed‐loop system is investigated using the Lyapunov direct method. Finally, theoretical developments are verified through numerical simulation.     

Event‐driven model predictive control of timed hybrid Petri nets

Hybrid Petri nets represent a powerful modeling formalism that offers the possibility of integrating, in a natural way, continuous and discrete dynamics in a single net model. Usual control approaches for hybrid nets can be divided into discrete‐time and continuous‐time approaches. Continuous‐time approaches are usually more precise, but can be computationally prohibitive. Discrete‐time approaches are less complex, but can entail mode‐mismatch errors due to fixed time discretization. This work proposes an optimization‐based event‐driven control approach that applies on continuous time models and where the control actions change when discrete events occur. Such an approach is computationally feasible for systems of interest in practice and avoids mode‐mismatch errors. In order to handle modelling errors and exogenous disturbances, the proposed approach is implemented in a closed‐loop strategy based on event‐driven model predictive control. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust optimal control of time‐delay systems based on Razumikhin theorem

This paper presents an optimal control approach for the general robust control design problem of linear time delay systems, which considers parameter uncertainties as well as state delay. It is shown that the robust control problem can be transformed into an optimal control problem with the amouof plant uncertainties involved in the performance index. A stability criterion has been developed under which the uncertain dynamical system can not only achieve stability, but also acquire the guaranteed level of performance for regulation. A suitable linear state feedback control law is also characterized via Lyapunov stability theory to ensure performance robustness of the closed‐loop system. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

H∞ fuzzy control design of discrete‐time nonlinear active fault‐tolerant control systems

This paper is concerned with the problem of H_∞ fuzzy controller synthesis for a class of discrete‐time nonlinear active fault‐tolerant control systems (AFTCSs) in a stochastic setting. The Takagi and Sugeno (T–S) fuzzy model is employed to exactly represent a nonlinear AFTCS. For this AFTCS, two random processes with Markovian transition characteristics are introduced to model the failure process of system components and the fault detection and isolation (FDI) decision process used to reconfigure the control law, respectively. The random behavior of the FDI process is conditioned on the state of the failure process. A non‐parallel distributed compensation (non‐PDC) scheme is adopted for the design of the fault‐tolerant control laws. The resulting closed‐loop fuzzy system is the one with two Markovian jump parameters. Based on a stochastic fuzzy Lyapunov function (FLF), sufficient conditions for the stochastic stability and H_∞ disturbance attenuation of the closed‐loop fuzzy system are first derived. A linear matrix inequality (LMI) approach to the fuzzy control design is then developed. Moreover, a suboptimal fault‐tolerant H_∞ fuzzy controller is given in the sense of minimizing the level of disturbance attenuation. Finally, a simulation example is presented to illustrate the effectiveness of the proposed design method. Copyright © 2008 John Wiley & Sons, Ltd.     

An impulsive‐switched‐system approach to aperiodic sampled‐data systems with time‐delay control

This paper devotes to the stability of aperiodic sampled‐data systems with time‐delay control, where the delays can impose a positive effect on the stability of the systems. The systems are modeled as impulsive switched systems with fixed switching laws. A novel separation theorem is presented to determine the Schur property of a matrix product and then used to obtain a less conservative stability criterion for the impulsive switched systems with fixed switching laws. By the separation theorem and a loop‐functional approach, some new stability and stabilization criteria for aperiodic sampled‐data systems with time‐delay control are provided in terms of linear matrix inequalities. Finally, the stability and stabilization results are tested on some classical numerical examples to illustrate the efficiency of the proposed method.