Fastest recovery after feedback disruption

The problem of quickly reducing operating errors during recovery from a feedback disruption is considered. The objective is to design controllers that reduce operating errors as quickly as possible, once feedback has been restored. It is shown that robust optimal feedback controllers that achieve this objective do exist. Furthermore, it is shown that the performance of optimal controllers can be approximated as closely as desired by controllers that generate bang–bang input signals for the controlled system. Controllers that generate bang–bang signals are relatively easy to derive and implement, since bang–bang signals are characterised by a finite list of scalars – their switching times.     

Fastest recovery after feedback disruption: nonlinear delay-differential systems

The problem of reducing operating errors after a feedback disruption is considered for a class of nonlinear delay-differential systems. It is shown that there are optimal controllers that reduce such errors in minimal time, once feedback has been restored. It is further shown that optimal performance can be approximated by bang-bang controllers – controllers that are easy to design and implement.     

Optimal robust control of nonlinear time-delay systems: Maintaining low operating errors during feedback outages

The problem of maintaining low operating errors during feedback outages is considered for a class of nonlinear systems with time-delays in the input channel. It is shown that there are optimal controllers that keep operating errors below a specified bound for the longest time possible. Furthermore, it is shown that optimal performance can be approximated as closely as desired by using bang-bang controllers – controllers that are relatively easy to calculate and implement.     

On discrete dynamic output feedback min-max controllers

The paper considers output feedback min-max controllers for non-square discrete time uncertain linear systems. Based on previous work, it is demonstrated that static output feedback min-max controllers are only realizable for a specific class of systems. To broaden this class, a compensator based framework is proposed to introduce additional degrees of freedom. The conditions for the existence of such dynamic output feedback min-max controllers are given and are shown to be relatively mild. Furthermore, a simple parameterization of the available design freedom is proposed. An explicit procedure is described which shows how a Lyapunov matrix, which satisfies both a discrete Riccati inequality and a structural constraint, can be obtained using Linear matrix inequality optimization. This Lyapunov matrix is used to calculate the robustness bounds associated with the closed-loop system. A simple aircraft example is provided to demonstrate the efficacy of the design approach.     

LQG optimal scalar static output feedback

An eigenproblem-based technique is given for computing the stabilizing scalar static output feedback gain that minimizes the standard linear quadratic performance index in the presence of a Gaussian white-noise disturbance. The method adapts recent work on eigenproblem-based computation of _∞-norms.     

Robust optimal control during feedback disruption for nonlinear systems controlled by an observer-based output feedback controller

In this paper, a robust optimal control problem during feedback disruption is considered for a class of nonlinear systems which have been controlled by an observer-based output feedback controller. It is shown that during feedback disruption, there exists an optimal control input which keeps both system states and observer errors within a specified bound for the longest time. Then, it is shown that such an optimal control input can be practically implemented by using a bang-bang control input in terms of control performance. One numerical and one practical examples are given for clear illustration.     

Bounded output feedback tracking control of fully actuated Euler-Lagrange systems

In this short note we deal with the problem of trajectory tracking control of fully actuated Euler-Lagrange systems with unmeasurable velocities and bounded control inputs. In order to avoid the use of velocity measurements we introduce a nonlinear dynamic extension for the plant which renders the closed-loop system semi-globally asymptotically stable, hence, we prove that by increasing some of the dynamic extension parameters it is possible to enlarge the domain of attraction and to maintain the control inputs bounded.     

Optimal exponential feedback stabilization of planar systems

This paper solves the problem of finding an optimal feedback control ensuring the maximal rate of convergence of system solutions to the origin for a general class of planar control systems including switched, bilinear systems and ones described by differential inclusions, etc. The prescribed control set is assumed to be compact but not necessarily convex. The developed approach is based on finding the minimal Lyapunov exponent of the system with an open loop control which provides an upper bound for the optimal convergence rate of the closed loop system. Then an optimal feedback controller is constructed for which the obtained bound is attained.     

A gradient flow approach to decentralised output feedback optimal control

This paper visits the quadratic optimal control problem of decentralised control systems via static output feedback. A gradient flow approach is introduced as a tool to compute the optimal output feedback gain. Several nice properties are revealed concerning the convergence of the gain matrix along the trajectory of an ordinary differential equation obtained from the gradient of objective cost, i.e. the objective cost is decreasing along this trajectory. If the equilibrium points are isolated, the convergence can be guaranteed. A simulation example is given to illustrate the effectiveness of this approach.     

Dynamic Output Feedback Robust MPC Using General Polyhedral State Bounds for the Polytopic Uncertain System With Bounded Disturbance

This paper considers the dynamic output feedback robust model predictive control (MPC) for a system with both polytopic model parametric uncertainty and bounded disturbance. For this topic, the techniques for handling the unknown true state are crucial, and the strict guarantee of the input/output/state constraints favors replacing the true state by its bound in the optimization problems. The previous utilized polyhedral bounds, constructed by virtue of the error signals which are some linear combinations of the true state, the estimated state and the output, are generalized, where a bias item is utilized. Based on this unified bounding approach, new techniques for handling the unknown true state are given for both the main and the auxiliary optimization problems. As before, the main optimization problem calculates the control law parameters conditionally, and the auxiliary optimization problem determines the time to refresh these parameters. By applying the proposed method, the augmented state of the closed‐loop system is guaranteed to converge to the neighborhood of the equilibrium point. A numerical example is given to illustrate the effectiveness of the new method.     

NBFI系统的稳定性分析

NBFI（基于网络的反馈连接）是一类基于网络反馈连接的系统。文中研究了此模型的数据包丢失的问题,将带有有界任意丢包问题的NBFI系统建模成一般的线性切换系统．并应用切换Lyapunov函数方法加以分析,进而给出了NBFI系统渐近稳定的充分条件．并将结果推广到单位时延的情况。最后给出仿真,从而验证了结论的正确性。     

Bounded smooth state feedback and a global separation principle for non-affine nonlinear systems

This paper develops sufficient conditions for a general nonlinear control system to be locally (resp. globally) asymptotically stabilizable via smooth state feedback. In particular, it is shown that as in the case of affine systems, this is possible if the unforced dynamic system of ∑₁ is Lyapunov stable and appropriate controllability-like rank conditions are satisfied. Our results incorporate a series of well-known stabilization theorems proposed in the literature for affine control systems and extend them to nonaffine nonlinear control systems.     

An algorithm to compute state feedback matrices for multi-input deadbeat control

An algorithm for the computation of a state feedback controller shifting all eigenvalues of the closed loop system to the origin is presented. The available freedom in multi-input systems is used to reduce the norm of the feedback matrix. The algorithm places one or more eigenvalues in each step using partial feedback laws of minimal norm. This results in an overall feedback matrix whose norm is close to its minimum value in most cases.     

Bounded Consensus Algorithms for Multi‐Agent Systems in Directed Networks

In this paper, the consensus problem is investigated via bounded controls for the multi‐agent systems with or without communication. Based on the nested saturation method, the saturated control laws are designed to solve the consensus problem. Under the designed saturated control laws, the transient performance of the closed‐loop system can be improved by tuning the saturation level. First of all, asymptotical consensus algorithms with bounded control inputs are proposed for the multi‐agent systems with or without communication delays. Under these consensus algorithms, the states’ consensus can be achieved asymptotically. Then, based on a kind of novel nonlinear saturation functions, bounded finite‐time consensus algorithms are further developed. It is shown that the states’ consensus can be achieved in finite time. Finally, two examples are given to verify the efficiency of the proposed methods.     

Stabilization with data-rate-limited feedback: tightest attainable bounds

This paper investigates the stabilizability of a linear, discrete-time plant with a real-valued output when the controller, which may be nonlinear, receives observation data at a known rate. It is first shown that, under a finite horizon cost equal to the mth output moment, the problem reduces to quantizing the initial output. Asymptotic quantization theory is then applied to directly obtain the limiting coding and control scheme as the horizon approaches infinity. This is proven to minimize a particular infinite horizon cost, the value of which is derived. A necessary and sufficient condition then follows for there to exist a coding and control scheme with the specified data rate that takes the mth output moment to zero asymptotically with time. If the open-loop plant is finite-dimensional and time-invariant, this condition simplifies to an inequality involving the data rate and the unstable plant pole with greatest magnitude. Analagous results automatically hold for the related problem of state estimation with a finite data rate.     

Dynamic output feedback control synthesis for stochastic time-delay systems

This article deals with the dynamic output feedback control synthesis problem for Itô-type stochastic time-delay systems. Our aim is to design a full order dynamic output feedback controller to achieve the desired control objectives. We will formulate the controller design problem as an H _∞ optimisation problem in the mean-square sense. The main contributions of this article are as follows: (i) for stochastic systems, the design of a controller with multiple objectives can be addressed without employing a unique Lyapunov function; (ii) using an inequality technique and Finsler Lemma, we provide convex controller synthesis conditions described by linear matrix inequalities (LMIs). Some examples are presented to show the effectiveness of the developed theoretical results.     

Discrete-time certainty equivalence output feedback: allowing discontinuous control laws including those from model predictive control

We present certainty equivalence output feedback results for discrete-time nonlinear systems that employ possibly discontinuous control laws in the feedback loop. Coupling assumptions of nominal robustness with uniform observability or detectability assumptions, we assert nominally robust stability for output feedback closed loops. We further show that model predictive control (MPC) can be used to generate a feedback control law that is robustly globally asymptotically stabilizing when used in a certainty equivalence output feedback closed loop. Allowing for discontinuous feedback control laws is important for systems employing MPC, since the method can, and sometimes necessarily does, result in discontinuous control laws.     

Suboptimal local feedback control for a class of constrained discrete time nonlinear control problems

In this paper, we consider a class of constrained discrete time optimal control problems involving general nonlinear dynamics with fixed terminal time. A method to solve the feedback control problem for a class of unconstrained continuous time nonlinear systems has been proposed previously. In that work, the solution is based on synthesizing an approximate suboptimal feedback controller locally in the neighbourhood of a certain nominal optimal trajectory. This paper expands on the same theme by considering problems involving discrete time systems. Taking advantage of the nature of discrete time systems, a further reduction on the computational effort of synthesising the feedback controller is made possible. Also, this paper extends the applicability of the method to constrained systems. For illustration, a numerical example is solved using the proposed method.     

Output feedback guaranteed cost control of networked linear systems with random packet losses

This article is concerned with the output feedback guaranteed cost control problem for a class of networked control systems (NCSs) with both packet losses and network-induced delays. The packet-loss processes in the forward channel and the backward channel are modelled as two Markov chains. The dynamic output feedback controllers are considered, and the closed-loop NCS is modelled as a discrete-time Markovian system with two modes and unit time delay. By using a properly constructed Lyapunov function and the state transformation technique, a sufficient condition is derived for the closed-loop NCS to be mean-square exponentially stable and ensure a decay rate that can be tuned according to the packet loss situations in the networks. Moreover, design procedures for the guaranteed cost controllers are also presented based on the obtained stability condition and guaranteed cost performance result. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed results.     

Robust optimal stabilization of the Brockett integrator via a hybrid feedback

The problem of semi-global minimal time robust stabilization of the Brockett integrator (also called Heisenberg system) is addressed and solved by means of a hybrid state feedback law. It is shown that the solutions of the closed-loop system converge to the origin, in quasi-minimal time (for a given bound on the controller), with a robustness property with respect to small measurement noises, external disturbances and actuator noises.