H∞‐output regulation of linear heterogeneous multiagent systems over switching graphs

In this paper, we analyze H_∞‐output regulation of linear heterogeneous multiagent systems. The agents are subject to modeled and unmodeled disturbances and communicate over a switching graph. We derive a sufficient condition that guarantees H_∞ output regulation for the mentioned setup. This sufficient condition places requirements on both the single‐agent systems and the switching graph. The requirement on the single‐agent systems is an H_∞‐criterion that should be satisfied by a proper design of the controller. Meanwhile, the switching graph needs to be maximally connected. Moreover, we derive an upper bound for the overall ‐gain of the output synchronization error with respect to the unmodeled disturbances over a fixed communication graph. We illustrate our technical developments by a simulation example.     

Semiglobal finite‐time synchronization of complex networks with stochastic disturbance via intermittent control

This paper focuses on the problem of semiglobal finite‐time synchronization of stochastic complex networks via an intermittent control strategy. By establishing a finite‐time criterion condition and a novel finite‐time ‐operator differential inequality, combined with convex techniques, some sufficient conditions are obtained to ensure finite‐time synchronization for stochastic complex networks with time delays. An effective controller is given to guarantee inner finite‐time synchronization, especially for a nondelayed dynamic system. This paper provides a simple controller. Finally, a numerical simulation is given to demonstrate the effectiveness of our results.     

An iterative approach for the discrete‐time dynamic control of Markov jump linear systems with partial information

The , and mixed dynamic output feedback control of Markov jump linear systems in a partial observation context is studied through an iterative approach. By partial information, we mean that neither the state variable x(k) nor the Markov chain θ(k) are available to the controller. Instead, we assume that the controller relies only on an output y(k) and a measured variable coming from a detector that provides the only information of the Markov chain θ(k). To solve the problem, we resort to an iterative method that starts with a state‐feedback controller and solves at each iteration a linear matrix inequality optimization problem. It is shown that this iterative algorithm yields to a nonincreasing sequence of upper bound costs so that it converges to a minimum value. The effectiveness of the iterative procedure is illustrated by means of two examples in which the conservatism between the upper bounds and actual costs is significantly reduced.     

Stability and stabilization for singularly perturbed systems with Markovian jumps

This article focuses on the stability and stabilization problems of singularly perturbed jump systems. Here, the singularly perturbed parameter (SPP) is also with Markov switching and satisfies any with positive bound predefined. First, stability conditions expressed ?_i‐free but involving its bound are developed by constructing an ?_i‐dependent Lyapunov function. Then, a method for state feedback stabilization controller depending on SPP is proposed, whose conditions are given in terms of linear matrix inequalities. Moreover, some special cases about deterministic SPP are considered too. Finally, two practical examples are used to demonstrate the effectiveness and superiorities of the proposed methods.     

Stochastic approximation with nondecaying gain: Error bound and data‐driven gain‐tuning

Our problem of interest is to minimize a sequence of scalar‐valued loss functions f_k(·) or to locate the root(s) of a sequence of vector‐valued functions g _k(·) corresponding to time with respect to a parameter . The available information for the minimization/root‐finding is the noise‐corrupted observation(s) of either f_k(·) or g _k(·) evaluated at a few of certain design points only. Taking both the dynamics and randomness into consideration, we use stochastic approximation (SA) algorithms to solve the time‐varying problem, but with a nondecaying gain (stepsize). The tracking performance of the nondecaying gain SA algorithm is guaranteed by a computable bound for the root‐mean‐squared error and mean‐absolute‐deviation. The only assumption imposed on the drifts is that the average distance between two consecutive underlying true parameters is bounded from above—this assumption allows the varying target to change abruptly. The error term arising from using the noisy evaluation of f_k(·) or g _k(·) in constructing the search direction is assumed to have bounded second‐moment—this allows for biased estimator to be used in the SA algorithms. Given the lenient assumptions on the drift and error term, the error bounds apply to a broad class of time‐varying scenarios and are useful for finite‐sample analysis. Since the tracking capability characterizes the average performance across all possible sample paths, it may not provide much guidance on the gain‐tuning strategies useful for one single run. Hence, we propose a data‐dependent gain‐tuning strategy based on estimating the Hessian information and the noise level. The adaptive rule is advantageous as it enables the step size to vary with information gathered during the progress of the estimation procedure.     

Optimal linear combination of sensors and actuators to enforce an interior conic open‐loop system

This paper presents techniques to linearly combine the sensor measurements and/or actuator inputs of a linear time‐invariant system to obtain a new system that is interior conic with prescribed bounds. In the optimal sensor combination problem, a desired system output is defined, and in the optimal actuator combination problem, a desired system input is defined, along with a frequency bandwidth in which the desired system input or output should be matched. The simultaneous optimal sensor and actuator combination problem includes desired system outputs and inputs. In all cases, the weighted or norm of the difference between the system with linearly combined sensors or actuators and the desired system is minimized while rendering the new system interior conic with prescribed bounds. The weighting transfer matrix used in the ‐ or ‐optimization problem is determined by the frequency bandwidth of interest. The individual sensor and actuator combination methods involve linear matrix inequality constraints and are posed as convex optimization problems, whereas the combined sensor and actuator method is an iterative procedure composed of convex optimization steps. Numerical examples illustrate superior tracking performance with the proposed sensor and actuator combination techniques over comparable techniques in the literature when implemented with a simple feedback controller. Robust asymptotic stability of the closed‐loop system to plant uncertainty is demonstrated in the numerical examples.     

Simultaneous design of AWC and nonlinear controller for uncertain nonlinear systems under input saturation

This article addresses a novel technique for the simultaneous design of a robust nonlinear controller and static anti‐windup compensator (AWC) for uncertain nonlinear systems under actuator saturation and exogenous bounded input. The system is presumed to have locally Lipschitz nonlinearities, time‐varying uncertainties (appearing both in the linear as well as nonlinear dynamics and both in the state in addition to the output equations), and external norm‐bounded inputs both in the state and the output equations. Several bilinear matrix inequality–based conditions are derived to simultaneously design the robust nonlinear controller and AWC gains for uncertain nonlinear systems by employing the Lyapunov functional, reformulated Lipschitz property, uncertainty bounds, linear parameter‐varying approach, modified local and global sector conditions, iterative linear matrix inequality algorithm, convex optimization procedure, and gain minimization. The proposed multiobjective AWC‐based dynamic robust nonlinear controller guarantees the mitigation of saturation effects, robustness against time‐varying parametric norm‐bounded uncertainties, the asymptotic stability of the closed‐loop nonlinear system under zero external disturbances, and the attenuation of disturbance effects under nonzero external disturbances. The effectiveness of the proposed AWC‐based dynamic robust nonlinear controller synthesis scheme is illustrated by simulation examples.     

A mixed numerical–analytical stable pseudo‐inversion method aimed at attaining an almost exact tracking

This paper considers the problem of computing the input u(t) of an internally asymptotically stable, possibly non‐minimum phase, linear, continuous time system Σ yielding a very accurate tracking of a pre‐specified desired output trajectory . The main purpose of the new approach proposed here is to alleviate some limitations that inherent the classical methods developed in the framework of the preview‐based stable inversion, which represents an important reference context for this class of control problems. In particular, the new method allows one to deal with arbitrary and possibly uncertain initial conditions and does not require a pre‐actuation. The desired output to be exactly tracked in steady state is here assumed to belong to the set of polynomials, exponential, and sinusoidal time functions. The desired transient response is specified to obtain a fast and smooth transition toward the steady‐state trajectory , without under and/or overshoot in the case of a set point reset. The transient control input u_t(t) is a priori assumed to be given by a piecewise polynomial function. Once has been specified, this allows the computation of the unknown u_t(t) as the approximate least squares solution of the Fredholm's integral equation corresponding to the explicit formula of the output forced response. The steady‐state input u_s(t) is analytically computed exploiting the steady‐state output response expressions for inputs belonging to the same set of . Copyright © 2013 John Wiley & Sons, Ltd.     

Stabilization of the planar vertical take-off and landing using nonlinear feedback control

This article presents a new control strategy for the well-known problem of the planar vertical take-off and landing. The total thrust is computed using a nonlinear feedback compensation so that the altitude reaches the desired altitude. The horizontal position x is then controlled by choosing the orientation angle as a smooth saturation function of x and . A proof of convergence is presented using a Lyapunov approach. The proposed control strategy is successfully tested in numerical simulations.     

Robust control of the Hill's problem with drag

There are significant advantages associated with the analysis of satellite trajectory control problems in the Hill's analysis framework. As with the circular restricted three‐body problem (CRTBP) equations, the Hill's equations support three‐dimensional “halo” orbits that require station‐keeping control. These orbits are typically in regions of space close to a libration point. In most cases these orbits are unstable, with drag effects introducing uncertain exogenous forces. A two‐degree‐of‐freedom control strategy is used to maintain a pre‐selected orbit and introduce a quantifiable robust stability margin. The control study presented is based on a time‐periodic state feedback law, and a time‐periodic feed‐forward control that is based on a linearized drag model. The efficacy of these ideas is demonstrated by simulation.     

Quasi‐time‐dependent asynchronous filtering for discrete time switched systems via the event triggering mechanism

This article is concerned with the quasi‐time‐dependent asynchronous filter design problem for a class of discrete‐time switched systems via the event‐triggering mechanism. Applying the quasi‐time‐dependent Lyapunov functions and the mode‐dependent average dwell time technique, an asynchronous filter is designed with a weighted performance index; the filter parameter matrices are quasi‐time‐dependent in each event‐triggering‐dependent sampling interval; both cases (Case 1: no more than one switching, Case 2: multiple switchings) are taken into account in this sampling interval, by which the assumption, that the maximal asynchronous period is not larger than the minimal dwell time, is relaxed in this article. Simulation examples are given to show the less conservatism and effectiveness of the proposed results.     

H∞ control for uncertain one‐sided Lipschitz nonlinear systems in finite frequency domain

The current article discusses the H_∞ disturbance attenuation control design problem for one‐sided Lipschitz systems in finite frequency domain. Models containing norm‐bounded parameter uncertainties, disturbances, and input nonlinearities are considered. By contrast to existing full frequency methods, the H_∞ controller is computed depending on the frequency ranges of disturbances. The finite frequency disturbance attenuation index is initially defined. Thanks to Finsler's lemma, sufficient and less conservative analysis conditions are also derived for the closed‐loop system. Then, synthesis conditions in the low, middle, and high frequency ranges as well as the whole frequency range, are formulated in terms of linear matrix inequalities. At last, to prove the effectiveness and the superiority of the proposed approach, a physical example is used and a comparative study is done.     

Reciprocal convex approach to output‐feedback control of uncertain LPV systems with fast‐varying input delay

Robust control of parameter‐dependent input delay linear parameter‐varying (LPV) systems via gain‐scheduled dynamic output‐feedback control is considered in this paper. The controller is designed to provide disturbance rejection in the context of the induced ‐norm or the norm of the closed‐loop system in the presence of uncertainty and disturbances. A reciprocally convex approach is employed to bound the Lyapunov‐Krasovskii functional derivative and extract sufficient conditions for the controller characterization in terms of linear matrix inequalities (LMIs). The approach does not require the rate of the delay to be bounded, hence encompasses a broader family of input‐delay LPV systems with fast‐varying delays. The method is then applied to the air‐fuel ratio (AFR) control in spark ignition (SI) engines where the delay and the plant parameters are functions of the engine speed and mass air flow. The objectives are to track the commanded AFR signal and to optimize the performance of the three‐way catalytic converter (TWC) through the precise AFR control and oxygen level regulation, resulting in improved fuel efficiency and reduced emissions. The designed AFR controller seeks to provide canister purge disturbance rejection over the full operating envelope of the SI engine in the presence of uncertainties. Closed‐loop simulation results are presented to validate the controller performance and robustness while meeting AFR tracking and disturbance rejection requirements.     

Exact bounds for robust stability of output feedback controlled fractional‐order systems with single parameter perturbations

This article investigates exact robust stability bounds of output feedback controlled fractional‐order systems with the commensurate order and single parameter perturbations in all system coefficient matrices. First, a sufficient and necessary condition for robust asymptotical stability of such systems is obtained by using the Kronecker product. Then the maximal upper bounds and minimum lower bounds for robust asymptotical stability are established, respectively, without conservatism by transforming such problems into checking whether the matrix with single parameter perturbations is nonsingular or not. Finally, two numerical examples are given to show the effectiveness of the proposed results.     

Stochastic stability and extended dissipativity analysis for uncertain neutral systems with semi‐Markovian jumping parameters via novel free matrix–based integral inequality

This paper investigates the issues of stochastic stability and extended dissipativity analysis for uncertain neutral systems with semi‐Markovian jumping parameters. A new criterion about the stochastic stability and extended dissipativity of uncertain neutral systems with semi‐Markovian jumping parameters is obtained based on the new Lyapunov‐Krasovskii functionals together with the introduced novel free matrix–based integral inequality. The major contribution of this study is that the stochastic stability and extended dissipativity concept for uncertain neutral systems with semi‐Markovian jumping parameters can be developed to simultaneously analyze the solutions of the L₂ ? L_∞ performance, H_∞ action, passivity behavior, and dissipativity by selecting different weighting matrices. Finally, several interesting numerical examples are provided to show the effectiveness and less conservatism of the proposed method.     

A multilevel sampled‐data approach for resilient navigation and control of autonomous systems

Autonomous systems are rapidly becoming an integrated part of the modern life. Safe and secure navigation and control of these systems present significant challenges in the presence of uncertainties, physical failures, and cyber attacks. In this paper, we formulate a navigation and control problem for autonomous systems using a multilevel control structure, in which the high‐level reference commands are limited by a saturation function, whereas the low‐level controller tracks the reference by compensating for disturbances and uncertainties. For this purpose, we consider a class of nested, uncertain, multiple‐input–multiple‐output systems subject to reference command saturation, possibly with nonminimum phase zeros. A multirate output‐feedback adaptive controller is developed as the low‐level controller. The sampled‐data (SD) design of this controller facilitates the direct implementation on digital computers, where the input/output signals are available at discrete time instances with different sampling rates. In addition, stealthy zero‐dynamics attacks become detectable by considering a multirate SD formulation. Robust stability and performance of the overall closed‐loop system with command saturation and multirate adaptive control are analyzed. Simulation scenarios for navigation and control of a fixed‐wing drone under failures/attacks are provided to validate the theoretical findings.     

Direct synthesis of reduced order H controllers for a class of multivariable plants

Given an nth order, -control input, p-measured output generalized plant, this article proposes a simple, direct approach to design an output feedback H controller with order satisfying for , or for . For this purpose, the output feedback H control problem is transformed into an H state feedback problem for an augmented generalized system. A class of plants for which this transformation always exists and the ensuing controller has order as above, is identified. As a result, for such plants, the reduced order H controller gains are found just by solving a simple linear matrix inequality problem used in state feedback based H control. The efficacy of the proposed approach is studied on some benchmark examples.     

New interpolation solution and application in system modeling and optimal control with prescribed distance to instability

We present a system theoretic interpretation of a two‐sided interpolation problem with a stable rational matrix U (interpolant) without constraints on its norm. It is known that all solutions U of that problem can be expressed as U = U _h+ U _p, where U _h ranges in the set of all solutions of the associated homogeneous problem, and U _p is a particular solution. We present a new solution for U _p and prove that it is actually the minimal ‐norm interpolant in the set of all interpolants. We apply these results in system modeling and in optimal control of one‐block plants, with a prescribed bound on the distance to instability of the closed‐loop system. The applications are illustrated by examples. Interesting connections to the augmented basic interpolation problem, to Nehari's problem, and to the stability of one‐block plants with multiple unstable invariant zeros are given. Copyright © 2015 John Wiley & Sons, Ltd.     

Sparse control for continuous-time systems

In this survey article, we give a comprehensive review of sparse control for continuous-time systems, called maximum hands-off control. The maximum hands-off control is the optimal control, for which we introduce fundamental properties such as necessary conditions, existence, and equivalence to the optimal control. We also show an efficient numerical computation algorithm for the maximum hands-off control based on the time discretization and ADMM (alternating direction method of multipliers). A numerical example is shown with an available MATLAB program.