Risk-Informed Model-Free Safe Control of Linear Parameter-Varying Systems

This paper presents a risk-informed data-driven safe control design approach for a class of stochastic uncertain nonlinear discrete-time systems.The nonlinear system is modeled using linear parameter-varying(LPV)systems.A model-based probabilistic safe controller is first designed to guarantee probabilisticλ-contractivity(i.e.,stability and invariance)of the LPV system with respect to a given polyhedral safe set.To obviate the requirement of knowing the LPV system model and to bypass identifying its open-loop model,its closed-loop data-based representation is provided in terms of state and scheduling data as well as a decision variable.It is shown that the variance of the closedloop system,as well as the probability of safety satisfaction,depends on the decision variable and the noise covariance.A minimum-variance direct data-driven gain-scheduling safe control design approach is presented next by designing the decision variable such that all possible closed-loop system realizations satisfy safety with the highest confidence level.This minimum-variance approach is a control-oriented learning method since it minimizes the variance of the state of the closed-loop system with respect to the safe set,and thus minimizes the risk of safety violation.Unlike the certainty-equivalent approach that results in a risk-neutral control design,the minimum-variance method leads to a risk-averse control design.It is shown that the presented direct risk-averse learning approach requires weaker data richness conditions than existing indirect learning methods based on system identification and can lead to a lower risk of safety violation.Two simulation examples along with an experimental validation on an autonomous vehicle are provided to show the effectiveness of the presented approach.

Finite-time Prescribed Performance Time-Varying Formation Control for Second-Order Multi-Agent Systems With Non-Strict Feedback Based on a Neural Network Observer

This paper studies the problem of time-varying formation control with finite-time prescribed performance for nonstrict feedback second-order multi-agent systems with unmeasured states and unknown nonlinearities.To eliminate nonlinearities,neural networks are applied to approximate the inherent dynamics of the system.In addition,due to the limitations of the actual working conditions,each follower agent can only obtain the locally measurable partial state information of the leader agent.To address this problem,a neural network state observer based on the leader state information is designed.Then,a finite-time prescribed performance adaptive output feedback control strategy is proposed by restricting the sliding mode surface to a prescribed region,which ensures that the closed-loop system has practical finite-time stability and that formation errors of the multi-agent systems converge to the prescribed performance bound in finite time.Finally,a numerical simulation is provided to demonstrate the practicality and effectiveness of the developed algorithm.

Adaptive Event-Triggered Time-Varying Output Group Formation Containment Control of Heterogeneous Multiagent Systems

In this paper,a class of time-varying output group formation containment control problem of general linear hetero-geneous multiagent systems(MASs)is investigated under directed topology.The MAS is composed of a number of tracking leaders,formation leaders and followers,where two different types of leaders are used to provide reference trajectories for movement and to achieve certain formations,respectively.Firstly,compen-sators are designed whose states are estimations of tracking lead-ers,based on which,a controller is developed for each formation leader to accomplish the expected formation.Secondly,two event-triggered compensators are proposed for each follower to evalu-ate the state and formation information of the formation leaders in the same group,respectively.Subsequently,a control protocol is designed for each follower,utilizing the output information,to guide the output towards the convex hull generated by the forma-tion leaders within the group.Next,the triggering sequence in this paper is decomposed into two sequences,and the inter-event intervals of these two triggering conditions are provided to rule out the Zeno behavior.Finally,a numerical simulation is intro-duced to confirm the validity of the proposed results.

Tensor Decomposition-Based Channel Estimation and Sensing for Millimeter Wave MIMO-OFDM V2I Systems

An integrated sensing and communication(ISAC)scheme for a millimeter wave(mmWave)multiple-input multiple-output orthogonal frequency division multiplexing(MIMO-OFDM)Vehicle-to-Infrastructure(V2I)system is presented,in which both the access point(AP)and the vehicle are equipped with large antenna arrays and employ hybrid analog and digital beamforming structures to compensate the path loss,meanwhile compromise between hardware complexity and system performance.Based on the sparse scattering nature of the mmWave channel,the received signal at the AP is organized to a four-order tensor by the introduced novel frame structure.A CANDECOMP/PARAFAC(CP)decomposition-based method is proposed for time-varying channel parameter extraction,including angles of departure/arrival(AoDs/AoAs),Doppler shift,time delay and path gain.Then leveraging the estimates of channel parameters,a nonlinear weighted least-square problem is proposed to recover the location accurately,heading and velocity of vehicles.Simulation results show that the proposed methods are effective and efficient in time-varying channel estimation and vehicle sensing in mmWave MIMOOFDM V2I systems.

Optimal Control of Nonlinear Systems Using Experience Inference Human-Behavior Learning

Safety critical control is often trained in a simulated environment to mitigate risk.Subsequent migration of the biased controller requires further adjustments.In this paper,an experience inference human-behavior learning is proposed to solve the migration problem of optimal controllers applied to real-world nonlinear systems.The approach is inspired in the complementary properties that exhibits the hippocampus,the neocortex,and the striatum learning systems located in the brain.The hippocampus defines a physics informed reference model of the realworld nonlinear system for experience inference and the neocortex is the adaptive dynamic programming(ADP)or reinforcement learning(RL)algorithm that ensures optimal performance of the reference model.This optimal performance is inferred to the real-world nonlinear system by means of an adaptive neocortex/striatum control policy that forces the nonlinear system to behave as the reference model.Stability and convergence of the proposed approach is analyzed using Lyapunov stability theory.Simulation studies are carried out to verify the approach.

The Jaffa Transform for Hessian Matrix Systems and the Laplace Equation

Hessian matrices are square matrices consisting of all possible combinations of second partial derivatives of a scalar-valued initial function. As such, Hessian matrices may be treated as elementary matrix systems of linear second-order partial differential equations. This paper discusses the Hessian and its applications in optimization, and then proceeds to introduce and derive the notion of the Jaffa Transform, a new linear operator that directly maps a Hessian square matrix space to the initial corresponding scalar field in nth dimensional Euclidean space. The Jaffa Transform is examined, including the properties of the operator, the transform of notable matrices, and the existence of an inverse Jaffa Transform, which is, by definition, the Hessian matrix operator. The Laplace equation is then noted and investigated, particularly, the relation of the Laplace equation to Poisson’s equation, and the theoretical applications and correlations of harmonic functions to Hessian matrices. The paper concludes by introducing and explicating the Jaffa Theorem, a principle that declares the existence of harmonic Jaffa Transforms, which are, essentially, Jaffa Transform solutions to the Laplace partial differential equation.

Group-Consensus of Hierarchical Containment Control for Linear Multi-Agent Systems

The existing containment control has been widely developed for several years, but ignores the case for large-scale cooperation. The strong coupling of large-scale networks will increase the costs of system detection and maintenance. Therefore, this paper is concerned with an extensional containment control issue, hierarchical containment control. It aims to enable a multitude of followers achieving a novel cooperation in the convex hull shaped by multiple leaders. Firstly, by constructing the three-layer topology, large-scale networks are decoupled. Then,under the condition of directed spanning group-tree, a class of dynamic hierarchical containment control protocol is designed such that the novel group-consensus behavior in the convex hull can be realized. Moreover, the definitions of coupling strength coefficients and the group-consensus parameter in the proposed dynamic hierarchical control protocol enhance the adjustability of systems. Compared with the existing containment control strategy, the proposed hierarchical containment control strategy improves dynamic control performance. Finally, numerical simulations are presented to demonstrate the effectiveness of the proposed hierarchical control protocol.

Two-Parameter Block Triangular Splitting Preconditioner for Block Two-by-Two Linear Systems

This paper proposes a two-parameter block triangular splitting(TPTS)preconditioner for the general block two-by-two linear systems.The eigenvalues of the corresponding preconditioned matrix are proved to cluster around 0 or 1 under mild conditions.The limited numerical results show that the TPTS preconditioner is more efficient than the classic block-diagonal and block-triangular preconditioners when applied to the flexible generalized minimal residual(FGMRES)method.

Event-Triggered Finite-Time H∞ Filtering for Discrete-Time Nonlinear Stochastic Systems

This paper addresses the problem of event-triggered finite-time H∞ filter design for a class of discrete-time nonlinear stochastic systems with exogenous disturbances. The stochastic Lyapunov-Krasoviskii functional method is adopted to design a filter such that the filtering error system is stochastic finite-time stable (SFTS) and preserves a prescribed performance level according to the pre-defined event-triggered criteria. Based on stochastic differential equations theory, some sufficient conditions for the existence of H∞ filter are obtained for the suggested system by employing linear matrix inequality technique. Finally, the desired H∞ filter gain matrices can be expressed in an explicit form.

Static Output Feedback H_∞ Controllers Design for Descriptor Linear Systems Based on LMI

This paper considers the design problem of static output feedback H ∞ controllers for descriptor linear systems with linear matrix inequality (LMI) approach. Necessary and sufficient conditions for the existence of a static output feedback H ∞ controller are given in terms of LMIs. Furthermore, the design method of H ∞ controllers is provided using the solutions to the LMIs.

ADAPTIVE TRACKING CONTROL FOR A CLASS OF NONLINEAR COMPOSITE SYSTEMS *

In this paper, the problem of adaptive tracking control for a class of nonlinear large scale systems with unknown parameters entering linearly is discussed. Based on the theory of input output linearization of nonlinear systems, direct adaptive control schemes are presented to achieve bounded tracking. The proposed control schemes are robust with respect to the uncertainties in interconnection structure as well as subsystem dynamics. A numerical example is given to illustrate the efficiency of this method.

ROBUST STABILIZATING FOR A OLASS OF UNOERTAIN NONLINEAR INTEROONNECTED SYSTEMS USING VARIABLE STRUCTURE CONTROL

The robust stabilizating control problem for a class of uncertain nonlinear large-scale systems is discussed. Based on the theory of both input/output (I/O) linearization and decentralized variable structure control (VSC),two-level and decentralized variable structure control laws for this kind of systems are presented respectively,which achieve asymptotically stabilization despite the uncertainties and disturbances. At last,sirnulation of the disturbed two-pendulum system is given to illustrate the feasibility of proposed technique.

使用《Linear Control Systems Engineering》的实践

本文介绍了使用原版教材《L inear Con trol Systems Engineering》、英语授课的教学实践及改革措施 ,提出了进一步的实施计划。

Resilient Time-Varying Formation-Tracking of Multi-UAV Systems Against Composite Attacks: A Two-Layered Framework

This paper studies the countermeasure design problems of distributed resilient time-varying formation-tracking control for multi-UAV systems with single-way communications against composite attacks,including denial-of-services(DoS)attacks,false-data injection attacks,camouflage attacks,and actuation attacks(AAs).Inspired by the concept of digital twin,a new two-layered protocol equipped with a safe and private twin layer(TL)is proposed,which decouples the above problems into the defense scheme against DoS attacks on the TL and the defense scheme against AAs on the cyber-physical layer.First,a topologyrepairing strategy against frequency-constrained DoS attacks is implemented via a Zeno-free event-triggered estimation scheme,which saves communication resources considerably.The upper bound of the reaction time needed to launch the repaired topology after the occurrence of DoS attacks is calculated.Second,a decentralized adaptive and chattering-relief controller against potentially unbounded AAs is designed.Moreover,this novel adaptive controller can achieve uniformly ultimately bounded convergence,whose error bound can be given explicitly.The practicability and validity of this new two-layered protocol are shown via a simulation example and a UAV swarm experiment equipped with both Ultra-WideBand and WiFi communication channels.

Global stabilizing controller design for linear time-varying systems and its application on BTT missiles

A parametric method for the gain-scheduled controller design of a linear time-varying system is given. According to the proposed scheduling method, the performance between adjacent characteristic points is preserved by the invariant eigenvalues and the gradually varying eigenvectors. A sufficient stability criterion is given by constructing a series of Lyapunov functions based on the selected discrete characteristic points. An important contribution is that it provides a simple and feasible approach for the design of gain-scheduled controllers for linear time-varying systems, which can guarantee both the global stability and the desired closed-loop performance of the resulted system. The method is applied to the design of a BTT missile autopilot and the simulation results show that the method is superior to the traditional one in sense of either global stability or system performance.

Robust Stability and Stabilization of Discrete Singular Systems with Interval Time-varying Delay and Linear Fractional Uncertainty

The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality （LMI） approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.

Robust Admissibility and Stabilization of Uncertain Singular Fractional-Order Linear Time-Invariant Systems

This paper addresses the robust admissibility problem in singular fractional-order continuous time systems. It is based on new admissibility conditions of singular fractional-order systems expressed in a set of strict linear matrix inequalities(LMIs). Then, a static output feedback controller is designed for the uncertain closed-loop system to be admissible. Numerical examples are given to illustrate the proposed methods.

BLOCK DIAGONAL FORM AND BLOCK DIAGONAL CONTROLLER OF NONLINEAR SYSTEMS

A block diagonal form about a nonlinear system is defined. Based on the de finition, a design method ca1led block diagonal controller (BDC) is proPOsed bo feedbacklinearization. Thus, a linearization design of a class of nonlinear system can be simply re-alized. The result of design has been proved by mathematical simulation of a certain anti-ship missile.

Parallel Control for Continuous-Time Linear Systems:A Case Study

In this paper,a new parallel controller is developed for continuous-time linear systems.The main contribution of the method is to establish a new parallel control law,where both state and control are considered as the input.The structure of the parallel control is provided,and the relationship between the parallel control and traditional feedback controls is presented.Considering the situations that the systems are controllable and incompletely controllable,the properties of the parallel control law are analyzed.The parallel controller design algorithms are given under the conditions that the systems are controllable and incompletely controllable.Finally,numerical simulations are carried out to demonstrate the effectiveness and applicability of the present method.Index Terms-Continuous-time linear systems,digital twin,parallel controller,parallel intelligence,parallel systems.

Delay-dependent H-infinity control for linear descriptor systems with delay in state

A deky-dependent H-infinity control for descriptor systems with a state-delayis investigated. The purpose of the problem is to design a linear memoryless state-feedbackcontroller such that the resulting closed-loop system is regular, impulse free and stable with anH-infinity norm bound. Firstly, a deky-dependent bounded real lemma(BRL) of the time-deky descriptorsystems is presented in terms of linear matrix inequalities(LMIs) by using a descriptor modeltransformation of the system and by taking a new Lyapunov-Krasovsii functional. The introducedfunctional does not require bounding for cross terms, so it has less conservation. Secondly, withthe help of the obtained bounded real lemma, a sufficient condition for the existence of a newdeky-dependent H-infinity state-feedback controller is shown in terms of nonlinear matrixinequalities and the solvability of the problem can be obtained by using an iterative algorithminvolving convex optimization. Finally, numerical examples are given to demonstrate theeffectiveness of the new method presented.