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This article explores a successive convex optimization method for solving a class of nonconvex programming problems subject to bilinear matrix inequality (BMI) constraints. In particular, many control issues can be boiled down to BMI problems, which are typically NP‐hard. To get out of the predicament, we propose a more relaxed feasible set to approximate the original one, based on which a local optimization algorithm is developed and its convergence is analyzed. As a case of application, we consider static output‐feedback control for uncertain systems with disturbances in restricted frequency intervals. In order to strengthen the disturbance‐rejection capability over the given frequency range, we establish sufficient and necessary analysis conditions via the generalized Kalman‐Yakubovich‐Popov lemma, under which the homogeneous polynomially parameter‐dependent technique is adopted to facilitate the design. Finally, several examples are given to demonstrate the efficiency of the results. [ABSTRACT FROM AUTHOR]

Solving nonlinear model predictive control problems in real time is still an important challenge despite of recent advances in computing hardware, optimization algorithms and tailored implementations. This challenge is even greater when uncertainty is present due to disturbances, unknown parameters or measurement and estimation errors. To enable the application of advanced control schemes to fast systems and on low‐cost embedded hardware, we propose to approximate a robust nonlinear model controller using deep learning and to verify its quality using probabilistic validation techniques. We propose a probabilistic validation technique based on finite families, combined with the idea of generalized maximum and constraint backoff to enable statistically valid conclusions related to general performance indicators. The potential of the proposed approach is demonstrated with simulation results of an uncertain nonlinear system. [ABSTRACT FROM AUTHOR]

Summary: The sector stability theorem is an intuitive condition for the stability of feedback loops that unifies many lines of research including robust control and the theory of passive and dissipative systems. Applying this theorem typically requires checking or enforcing sector bounds on linear time‐invariant systems. This article discusses practical and efficient numerical methods for performing these tasks. We derive a frequency‐domain test for sector boundedness and use it to develop O(n3) numerical algorithms for computing the relative or directional indices of sector bounds. We also discuss how such algorithms can be combined with nonsmooth optimization techniques to enforce sector bounds while designing and tuning controllers. Several application examples illustrate the potential of these tools and techniques. [ABSTRACT FROM AUTHOR]

Summary: The loss of measurements used for controller scheduling or envelope protection in modern flight control systems due to sensor failures leads to a challenging fault‐tolerant control law design problem. In this article, an approach to design such a robust fault‐tolerant control system, including full envelope protections using multiobjective optimization techniques, is proposed. The generic controller design and controller verification problems are derived and solved using novel multiobjective hybrid genetic optimization algorithms. These algorithms combine the multiobjective genetic search strategy with local, single‐objective optimization to improve convergence speed. The proposed strategies are applied to the design of a fault‐tolerant flight control system for a modern civil aircraft. The results of an industrial controller verification and validation campaign using an industrial benchmark simulator are reported. [ABSTRACT FROM AUTHOR]

Summary: We introduce a new robust stability measure for systems with multiple pointwise delays, which is called smoothed spectral abscissa, consistently with the existing measure for delay‐free systems. Its main characteristics are that it is smooth with respect to the system parameters and it provides a trade‐off between the decay rate of the system solution and the H2 norm of a transfer matrix related with the system. The smoothed spectral abscissa is implicitly defined in terms of the H2 norm of an auxiliary system, and its computation is based on the so‐called delay Lyapunov matrix. We show that these features make the smoothed spectral abscissa suitable for the design of robust controllers by using standard gradient‐based optimization techniques and exploiting a novel characterization of the derivatives of the delay Lyapunov matrix with respect to the system parameters. [ABSTRACT FROM AUTHOR]

Summary: This paper presents the design of a new adaptive optimization‐based second‐order sliding mode control algorithm for uncertain nonlinear systems. It is designed on the basis of a second‐order sliding mode control with optimal reaching, with the aim of reducing the control effort while maintaining all the positive aspects in terms of finite‐time convergence and robustness in front of matched uncertainties. These features are beneficial to guarantee good performance in case of vehicle dynamics control, a crucial topic in the light of the increasing demand of semiautonomous and autonomous driving capabilities in commercial vehicles. The new proposal is theoretically analyzed, as well as verified relying on an extensive comparative study, carried out on a realistic simulator of a 4‐wheeled vehicle, in the case of a lateral stability control system. [ABSTRACT FROM AUTHOR]

Summary: A new robust controller design method that satisfies the H∞ criterion is developed for linear time‐invariant single‐input single‐output (SISO) systems. A data‐driven approach is implemented in order to avoid the unmodeled dynamics associated with parametric models. This data‐driven method uses fixed‐order controllers to satisfy the H∞ criterion in the frequency domain. The necessary and sufficient conditions for the existence of such controllers are presented by a set of convex constraints. These conditions are also extended to systems with frequency‐domain uncertainties in polytopic form. It is shown that the upper bound on the weighted infinity norm of the sensitivity function converges monotonically to the optimal value, when the controller order increases. Additionally, the practical issues involved in computing fixed‐order rational H∞ controllers in discrete‐time or continuous‐time by convex optimization techniques are addressed. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Summary: This paper focuses on spatially distributed control systems where the controller sensing and actuation topology is inherited from that of the plant. Specifically, this paper considers distributed systems composed of discrete‐time linear parameter‐varying subsystems interconnected over general graph structures. These distributed systems are subject to a communication latency of one sampling period, where the information sent by a subsystem at the current time step is received by the target subsystem at the next time step. Analysis and synthesis conditions are derived for control design in this setting using a parameter‐dependent Lyapunov approach with the ℓ2‐induced norm as the performance measure. Fast and easy‐to‐implement algorithms are also provided for constructing the controller in real time. The techniques developed are finally applied to a leader‐follower formation problem with intermittent communications. [ABSTRACT FROM AUTHOR]

Summary: In this work, we study the mixed H 2 / H ∞ control for Markov jump linear systems with hidden Markov parameters. The hidden Markov process is denoted by ( θ ( k ) , θ ^ ( k ) ), where the nonobservable component θ(k) represents the mode of operation of the system, whereas θ ^ ( k ) represents the observable component provided by a detector. The goal is to obtain design techniques for mixed H 2 / H ∞ control problems, with the controllers depending only on the estimate θ ^ ( k ), for problems formulated in 3 different forms: (i) minimizing an upper bound on the H 2 norm subject to a given restriction on the H ∞ norm; (ii) minimizing an upper bound on the H ∞ norm, while limiting the H 2 norm; and (iii) minimizing a weighted combination of upper bounds of both the H 2 and H ∞ norms. We propose also new conditions for synthesizing robust controllers under parametric uncertainty in the detector probabilities and in the transition probabilities. The so‐called cluster case for the mixed H 2 / H ∞ control problem is also analyzed under the detector approach. The results are illustrated by means of 2 numerical examples. [ABSTRACT FROM AUTHOR]

Summary: This paper aims at developing a robust observer–based estimated state feedback control design method for an uncertain dynamical system that can be represented as a linear time‐invariant system connected with an integral quadratic constraint–type nonlinear uncertainty. Traditionally, in existing design methodologies, a convex semidefinite constraint is obtained at the cost of conservatism and unrealistic assumptions. This paper avoids such assumptions and formulates, the design of the robust observer state feedback controller as the feasibility problem of a bilinear matrix inequality (BMI) constraint. Unfortunately, the search for a feasible solution of a BMI constraint is an NP‐hard problem in general. The applicability of a linearization method, such as the variable change method and the congruence transformation, depends on the specific structure of the problem at hand and cannot be generalized. This paper transforms the feasibility analysis of the BMI constraint into an eigenvalue problem and applies the convex‐concave–based sequential linear matrix inequality optimization method to search for a feasible solution. Furthermore, an augmentation of the sequential linear matrix inequality algorithm to improve its numerical stability is presented. In the application part, a vehicle lateral control problem is presented to demonstrate the applicability of the proposed algorithm to a real‐world estimated state feedback control design problem and the necessity of the augmentation for numerical stability. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of probabilistic robust stabilization for uncertain systems subject to input saturation. A new probabilistic solution framework for robust control analysis and synthesis problems is addressed by a scenario optimization approach, in which the uncertainties are not assumed to be norm bounded. Furthermore, by expressing the saturated linear feedback law on a convex hull of a group of auxiliary linear feedback laws, we establish conditions under which the closed-loop system is probabilistic stable. Based on these conditions, the problem of designing the state feedback gains for achieving the largest size of the domain of attraction is formulated and solved as a constrained optimization problem with linear matrix inequality constraints. The results are then illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

This paper deals with the design of a robust sliding mode-based extremum-seeking controller aimed at the online optimization of a class of uncertain reaction systems. The design methodology is based on an input-output linearizing method with variable-structure feedback, such that the closed-loop system converges to a neighborhood of the optimal set point with sliding mode motion. In contrast with previous extremum-seeking control algorithms, the control scheme includes a dynamic modelling-error estimator to compensate for unknown terms related with model uncertainties and unmeasured disturbances. The proposed online optimization scheme does not make use of a dither signal or a gradient-based optimization algorithm. Practical stabilizability for the closed-loop system around to the unknown optimal set point is analyzed. Numerical experiments for two nonlinear processes illustrate the effectiveness of the proposed robust control scheme. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper investigates the robust stability and performance of uncertain linear time-varying (LTV) systems using an integral quadratic constraint (IQC) based analysis approach. Specifically, previous theoretical work on IQC-based robustness analysis of linear time-invariant (LTI) systems is extended to discrete-time LTV systems. In the case of a general LTV nominal system, the analysis solution is provided in terms of an infinite-dimensional convex optimization problem. This optimization problem reduces into a finite-dimensional semidefinite program when the nominal system in question is finite horizon, periodic, or, more generally, eventually periodic. Finally, the results are applied to an unmanned aircraft control system executing an aggressive maneuver, where the developed techniques are used to find the region in which the aircraft is guaranteed to reside at the end of its planned trajectory. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper concerns the simulation of a class of nonlinear continuous-time systems under a set of initial conditions described by an ellipsoid. By getting inspiration from Lyapunov theory, we show that it is possible to derive a procedure allowing the computation of a bounding ellipsoidal envelope, which will enclose all the states that can be reached from the set of initial conditions. This numerical procedure is based on convex optimization, and it makes it possible to set a guaranteed hard bound on the evolution of the state of the system for all the possible initial conditions. At the end of the paper, we show an application of the method through an academic example. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper describes a nonlinear programming-based robust design methodology for controllers and prefilters of a predefined structure for the linear time-invariant systems involved in the quantitative feedback theory. This controller and prefilter synthesis problem is formulated as a single optimization problem with a given performance optimization objective and constraints enforcing stability and various specifications usually enforced in the quantitative feedback theory. The focus is set on providing constraints expression that can be used in standard nonlinear programming solvers. The nonlinear solver then computes in a single-step controller and prefilter design parameters that satisfy the prescribed constraints and maximizes the performance optimization objective. The effectiveness of the proposed approach is demonstrated through a variety of difficult design cases like resonant plants, open-loop unstable plants, and plants with variation in the time delay. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Time delay is frequently encountered in practical quantum feedback control systems with long transmission lines and measurement process. This paper is concerned with measurement-based feedback H ∞ control for quantum systems with time delays appearing in the feedback loops. A physical model is presented for the quantum time-delay system described by complex quantum stochastic differential equations. Quantum versions of some fundamental properties, such as dissipativity and stability, are discussed for this model. A numerical procedure is proposed for H ∞ controller synthesis, which can deal with a non-convex optimization problem arising in the design processes. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A new design method of PID structured controllers to achieve robust performance is developed. Both robust stabilization and performance conditions are losslessly expressed by bilinear constraints in the proportional-double derivative variable ( k P, k D D) and the integral-derivative variable ( k I, k D). Therefore, the considered control design can be efficiently solved by alternating optimization between ( k P, k D D) and ( k I, k D), which is a 2D computationally tractable program. The proposed method works equally efficiently whenever even higher order differential or integral terms are included in PID control to improve its robustness and performance. Numerical examples are provided to show the viability of the proposed development. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is concerned with the [ABSTRACT FROM AUTHOR]

This paper proposes a consensus protocol for a class of high-order multiagent systems under directed networks. It is supposed that each agent is exposed to an external disturbance additive to its control input. Based on the [ABSTRACT FROM AUTHOR]

Chatter is an instability phenomenon in high-speed milling that limits machining productivity by the induction of tool vibrations, inferior machining accuracy, noise, and wear of machine components. In this paper, a fixed-structure active chatter control design methodology is proposed, which enables dedicated shaping of the chatter stability boundary such that working points of higher machining productivity become feasible while avoiding chatter. The control design problem is cast into a nonsmooth optimization problem, which is solved using bundle methods. Using this approach, fixed-structure dynamic (delayed) output feedback controllers can be synthesized. Distinct benefits of this approach are the a priori fixing of the controller order, the limitation of the control action, and the fact that no finite-dimensional model approximations and online chatter estimation techniques are required. All these benefits are important in milling practice. Representative examples illustrate the power of the proposed methodology in terms of increasing the chatter-free depth of cut, thereby enabling significant increases in machining productivity. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY Based on recent papers that have demonstrated that robust iterative learning control can be based on parameter optimization using either the inverse plant or gradient concepts, this paper presents a unification of these ideas for discrete-time systems that not only retains the convergence properties and the robustness properties derived in previous papers but also permits the inclusion of filters in the input update formula and a detailed analysis of the effect of non-minimum-phase dynamics on algorithm performance in terms of a 'plateauing' or 'flat-lining' effect in the error norm evolution. Although the analysis is in the time domain, the robustness conditions are expressed as frequency domain inequalities. The special case of a version of the inverse algorithm that can be used to construct a robust stable anti-causal inverse non-minimum-phase plant is presented and analysed in detail. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]