Risk-sensitive large-population linear-quadratic-Gaussian Games with major and minor agents

This paper studies large-population dynamic games involving a linear-quadratic-Gaussian (LQG) system with an exponential cost functional. The parameter in the cost functional can describe an investor's risk attitude. In the game, there are a major agent and a population of $N$ minor agents where $N$ is very large. The agents in the games are coupled via both their individual stochastic dynamics and their individual cost functions. The mean field methodology yields a set of decentralized controls, which are shown to be an $ϵ$-Nash equilibrium for a finite $N$ population system where $ϵ=O\left(\frac{1}{\sqrt{N}}\right)$. Numerical results are established to illustrate the impact of the population's collective behaviors and the consistency of the mean field estimation.     

Distributed dynamic matrix control with constrained optimization for collision and obstacle avoidance of simulated multiple quadcopters

A system of fast moving quadcopters has a high risk of collisions with neighboring quadcopters or obstacles. The objective of this work is to develop a control strategy for collision and obstacle avoidance of multiple quadcopters. In this paper, the problem of distributed dynamic matrix control (DMC) for collision avoidance among a team of multiple quadcopters attempting to reach consensus in the horizontal plane and yaw direction ( $x,y$, and $\psi$) is investigated. Violations of a predetermined safety radius generates output constraints on the DMC optimization function, which has not been dealt with in the literature. Different from past works, the proposed strategy can perform collision avoidance in the $x$, $y$, and $z$-directions. In addition, logarithmic barrier functions are implemented as input rate constraints on the control actions. Extensive simulation studies for a team of quadcopters illustrate promising results of the proposed control strategy and case variations. In addition, DMC parameter effects on the system performance are studied, and a successful study for obstacle avoidance is presented.     

On the regional control problem of the bilinear wave equation

The present research deals with regional optimal control problem of the bilinear wave equation evolving on a spatial domain $\mathrm{\Omega }\subset {\mathrm{ℝ}}^n,n\ge 1$. Such an equation is excited by bounded controls that act on the velocity term. It addresses the tracking of a desired state all over the time interval $[0,T]$ only on a subregion $\omega$ of $\mathrm{\Omega }$ with minimum energy. Then, we prove that an optimal control exists and is characterized as a solution to an optimality system. Algorithm for the computation of such a control is given and successfully illustrated through simulations.     

Bifurcation and control of disease spreading networks model with two delays

In this paper, the dynamical behaviors are investigated for a complex network with two independent delays. Instead of taking time delays as bifurcation parameters, we choose probability $p$ and parameter $\mu$ as the control parameters to study their effects on local stability and Hopf bifurcation, respectively. Moreover, the conditions for generating Hopf bifurcation are given. Furthermore, we further discuss the effects of two time delays on the critical values of parameters $p$ and $\mu$. Finally, numerical simulations are used to illustrate the validity of the obtained results.     

Dynamic event-triggered distributed interval functional observers for interconnected systems

In this paper, we design dynamic event-triggered interval functional observers (FOs) for interconnected systems comprising $M$ $(M\ge 2)$ subsystems where each subsystem is subject to nonlinearities and output disturbances. Our design method consists of two main steps. First, we design decentralized dynamic event-triggered mechanisms (ETMs) which use only locally measured output information. We then consider the design of distributed interval FOs by using the newly proposed ETMs. Their existence conditions are established and formulated in terms of linear programming. We also derive a bound on the estimated error vector and show that this bound is the smallest. Thus, this ensures that the unknown linear functional state vector can be estimated within an upper and lower bound of its true value by the designed interval observers. Finally, we apply the obtained results to design dynamic event-triggered interval observers for linear functions of the state vectors of an $N$-machine power system.     

Gradient-free algorithms for distributed online convex optimization

In this paper, we consider the distributed bandit convex optimization of time-varying objective functions over a network. By introducing perturbations into the objective functions, we design a deterministic difference and a randomized difference to replace the gradient information of the objective functions and propose two classes of gradient-free distributed algorithms. We prove that both the two classes of algorithms achieve regrets of $O(T^{3/4})$ for convex objective functions and $O(T^{2/3})$ for strongly convex objective functions, with respect to the time index $T$ and consensus of the estimates established as well. Simulation examples are given justifying the theoretical results.     

Controllability of fractional dynamical systems with distributed delays in control using ψ-Caputo fractional derivative

This research investigates the controllability of linear and non-linear fractional dynamical systems with distributed delays in control using the $\psi$-Caputo fractional derivative. For controllability of linear systems, the positive definiteness of Grammian matrix, which is characterized by Mittag–Leffler functions, is used to provide necessary and sufficient conditions. For the controllability of non-linear systems, the iterative technique with the completeness of $X$ is used to obtain sufficient conditions. Using the $\psi$-Caputo fractional derivative, this study is new since it investigates the ideas of controllability. A couple of numerical results are offered to explain the theoretical results.     

An optimal robust design method for fractional-order reset controller

In this paper, a novel design method for the reset controller structure (i.e., fractional-order proportional and integral plus Clegg integrator (PI ${}^{\alpha }$ + CI ${}^{\alpha }$)), is proposed for a second-order plus time delay plant. To this end, the designer can get an optimal fractional reset controller that gives the control system more phase margin over the base linear PI controller and robust to loop gain variation. The describing function method is used to investigate the capability of phase lead and the frequency domain properties of PI ${}^{\alpha }$ + CI ${}^{\alpha }$. The gain crossover frequency and phase margin specifications ensure the stability of the control system, and the flat phase constraint makes the control system robust to loop gain variations. Meanwhile, the integral of time and absolute error (ITAE) value is applied to achieve the optimal dynamic performance as the cost function. PI ${}^{\alpha }$ + CI ${}^{\alpha }$ is compared with its integer-order counterpart (i.e., proportional and integral plus Clegg integrator (PI + CI) controller) and their base controllers (i.e., integer-order PI and fractional-order PI controllers) in terms of the step response and robustness to loop gain variations. The simulation results illustrate that the PI ${}^{\alpha }$ + CI ${}^{\alpha }$ control system obtains lower overshoot and oscillation and better robustness to loop gain variations than others. The experiments are performed on the speed control of an air bearing stage. Experimental results show that the designed PI ${}^{\alpha }$ + CI ${}^{\alpha }$ control system behaves better than others. The proposed PI ${}^{\alpha }$ + CI ${}^{\alpha }$ design method can be applied to other general control plants easily.     

Linear Diophantine equation (LDE) decoder: A training-free decoding algorithm for multifrequency SSVEP with reduced computation cost

Multifrequency steady-state visual evoked potentials (SSVEPs) have been developed to extend the capability of SSVEP-based brain-machine interfaces (BMIs) to complex applications that have large numbers of targets. Even though various multifrequency stimulation methods have been introduced, the decoding algorithms for multifrequency SSVEP are still in early development. The recently developed multifrequency canonical correlation analysis (MFCCA) was shown to be a feasible training-free option to use in decoding multifrequency SSVEPs. However, the time complexity of MFCCA is shown to be $O(n^3)$, which will lead to long computation time as $n$ grows, where $n$ represents the input size in decoding. In this paper, a novel decoding algorithm is proposed with the aim to reduce the time complexity. This algorithm is based on linear Diophantine equation solvers and has a reduced computation cost $O(nlogn)$ while remaining training-free. Our simulation results demonstrated that linear Diophantine equation (LDE) decoder run time is only one fifth of MFCCA run time under respective optimal settings on 5-s single-channel data. This reduced computation cost makes it easier to implement multifrequency SSVEP in real-time systems. The effectiveness of this new decoding algorithm is validated with nine healthy participants when using dry electrode scalp electroencephalography (EEG).     

Adaptive neural network fixed-time control of p$$ p $$-normal systems with asymmetric output constraints

This paper studies the problem of fixed-time $H_{\infty }$ control for a class of nonlinear $p$-normal systems with asymmetric output constraints and external disturbances. Compared with the existing fixed-time control schemes, the smooth switching functions are designed to avoid the singularity problem. Then, a time-varying nonlinear transformation function (NTF) is introduced, blue and a unified tool to deal with the symmetric, asymmetric, and even unconstrained problems simultaneously. Moreover, by adding blue one power integration technology, the $H_{\infty }$ controller is designed, which can inhibit the influence of external disturbances on the system. According to Lyapunov stability analysis, the presented fixed-time $H_{\infty }$ blue control method ensures that all signals are bounded in a fixed time. In the end, two simulation examples demonstrate the effectiveness of the proposed scheme.     

Lumped uncertainty alleviation in output channels of MIMO nonlinear systems based on robust disturbance observer-based control strategy

Disturbances and uncertainties can produce unsatisfactory responses in many industrial and engineering systems. Besides, the practical systems and processes are multiple-input multiple-output (MIMO). Hence, achieving a good control performance with adequate output responses is not simple. Many different methods were provided for control of industrial processes in some references. However, in this paper, the primary goal is to design an appropriate tracking controller for alleviating the destructive effects of uncertainties in output channels of MIMO nonlinear systems. For this purpose, a robust mechanism has been introduced according to the optimal design of centralized extended proportional-derivative (CEPD) and disturbance observer (DOB). By designing the derivative part $K_d$ based on famous Vandermonde matrix and DOB gain $\mathrm{\Gamma }$, the robust criterion $R={\left(I+CG{K}_d\right)}^{-1}$ is obtained to tackle the undesirable factors such as nonlinear functions and uncertainties in error dynamics. The closed-loop stability is guaranteed by tuning the proportional part $K_p$ under linear matrix inequality. The proposed scheme in this paper can be used for a wide range of MIMO nonlinear systems in practical situations.     

An improved output feedback controller design for linear discrete-time systems using a matrix decomposition method

This paper presents the design of output feedback controllers for discrete-time (DT) linear systems. New sufficient LMI conditions are derived for designing static $H_2$ and $H_{\infty }$ controllers using decomposition of an auxiliary matrix. The decomposition facilitates linearization of nonlinear term of reduced size to obtain linear matrix inequality criteria. This leads to less conservative results as shown in the numerical examples. In addition, the proposed static output feedback criteria is also used for designing dynamic output feedback controllers for DT systems. Furthermore, a comparative study is also made for the proposed design method with the results existing in the literature. Finally, a DT static output feedback $H_{\infty }$ controller is designed for a quarter-car suspension system. Simulation results are provided to show the efficacy of the proposed design method.     

Interval estimation and fault detection for switched nonlinear systems based on zonotope method

This paper investigates the state interval estimation and fault detection (FD) problems for a Lipschitz nonlinear switched system based on the combination of the $H_{\infty }$ observer and the zonotope method. To begin with, an $H_{\infty }$ observer that is robust to the disturbance is designed, and the stability of the observer error dynamic system is analyzed under the average dwell time (ADT) concept. After this, the zonotope theory is applied on the $H_{\infty }$ observer error dynamic system such that the interval state estimation can be calculated iteratively when the system suffers from no fault. Furthermore, for FD purpose, a residual is constructed based on the $H_{\infty }$ observer. Because the constructed residual contains disturbance, it cannot be used for FD directly. To overcome this drawback, the interval estimation method of the residual is proposed by using the zonotope method, and a residual-based FD scheme is developed. Finally, a simulation example is given to verify the effectiveness of the proposed method.     

Remark on stability margin of Lur'e systems

In a recent work, a definition of stability margin (gain and phase margins) for a class of nonlinear systems (Lur'e systems consisting of a linear time-invariant (LTI) plant and a sector-constrained nonlinearity) is proposed based on the famous circle criterion. This definition is indeed interesting because the concept of gain and phase margins has been largely limited to linear systems with a single input and a single output (SISO), but it was further established for Lur'e systems with a particular type of sector constraints ( $k_1=0$, e.g., saturation). In this paper, the previously established concept is extended to cover Lur'e systems with a general type of sector constraints ( $k_1\ge 0$). It is, however, pointed out that in case of $k_1=0$, the definitions of phase margin based on the circle criterion can be misleading and need to be modified or replaced perhaps by a time-delay margin for Lur'e systems including an integrator, for which the phase margin can be trivially zero.     

Observer-based finite-time H∞ control of Itô-type stochastic nonlinear systems

This paper investigates the finite-time $H_{\infty }$ control of Itô-type stochastic nonlinear systems. Considering the transient performance and anti-interference ability within a given limited time interval, the control strategy of stochastic nonlinear systems is researched. A new sufficient condition for mean-square finite-time boundedness for stochastic nonlinear system is developed. Due to the state components are not available, a state observer is designed. Based on the estimated state, an $H_{\infty }$ controller is proposed and Linear Matrix Inequality (LMI) conditions are given, which not only guarantee the mean-square finite-time boundedness but also satisfy the corresponding $H_{\infty }$ performance. Finally, two examples are given to demonstrate the effectiveness of the results.     

H∞ filtering for continuous fractional-order 2D Roesser model: The 0<α≤1 case

This paper investigates the $H_{\infty }$ filtering for the continuous fractional-order (FO) two-dimensional (2D) Roesser model with the FO between 0 and 1. Firstly, a sufficient condition to ensure the stability and bounded realness in the sense of $H_{\infty }$-norm for the continuous FO 2D Roesser model is given in the form of linear matrix inequalities (LMIs). Secondly, based on the bounded real lemmas proposed above, the $H_{\infty }$ filtering problem for continuous FO 2D Roesser model is addressed through some congruent transformation and matrix transformation. The results are given in LMI form, and the parameters of the continuous FO 2D filters can be achieved from the LMIs easily. In the end, the effectiveness of the proposed results is verified by two numerical examples.     

Active fault detection and isolation in linear time-invariant systems: A geometric approach

In this work, a novel approach on active fault detection and isolation for linear time-invariant systems, named forced diagnosability, is proposed. This approach computes a continuous state feedback law to render a fault diagnosable, even when it cannot be diagnosed by using passive diagnosis methods. To do that, this work derives novel geometric relationships between unobservability and $(A,B)$-invariant subspaces that, under certain conditions, guarantee the existence of such state feedback law. The objective of the state feedback law is to force all the faults, except the one required to be diagnosed, named $L_d$, to reside in an unobservability subspace. This effectively decouples the effect of $L_d$ on the system output, from the effect of the other faults, allowing the design of a residual generator to detect and isolate the desired fault. The proposed state feedback law continuously forces diagnosability, and it can be computed in polynomial time. This avoids testing faults only at fixed time intervals and solving complex optimization problems required in other active diagnosis approaches. A numerical example is presented to illustrate the efficiency of the proposed approach.     

Observer-based path following control for autonomous vehicles with localization errors and tire slip effects

This paper investigates the problem of path following control for an autonomous vehicle subject to the localization errors and the tire slip effects. First, by analyzing the effects of localization errors, a loss-of-effectiveness actuator model is formulated, and a new chain form model is constructed for path following system of the vehicle. Then, the polytopic model is proposed to characterize the nonlinearity of the system, and an observer-based path following controller is designed by satisfying both the $H_{\infty }$ criterion and $L_1$ criterion. Finally, the path following controller design problem is converted into an optimization problem, which can be solved readily through convex optimization techniques. The effectiveness of the proposed control strategy is verified by simulation results.     

Two-channel false data injection attacks on multi-sensor remote state estimation

This paper investigates a security problem in cyber-physical systems (CPSs) under multisensory framework. In the considered system, the feedback and feed-forward channels may suffer from false data injection (FDI) attacks. The attacker aims at disturbing the systems by modifying the sensors' measurements and injecting external control inputs while keep ( $ϵ,\delta$)-stealthiness. Two types of multi-sensor fusion Kalman filters, which are equivalent in the absence of attacks, are adopted by the remote state estimator. When the system is maliciously attacked, the necessary and sufficient condition is obtained to guarantee the equivalence of the sequential Kalman filter and data compression Kalman filter under two-channel attacks. Moreover, suboptimal ( $ϵ,\delta$)-stealthiness attack strategies for these Kalman filters are obtained by applying two-stage optimization method, convex analysis and monotonic optimization techniques. Finally, simulations on a numerical example of a quadrotor are carried out to validate the feasibility of theoretical results.