Bounded Disturbances Research Articles

Stealthy Attacks and Robust Detectors for Cyber-Physical Systems with Bounded Disturbances: A Zonotope Approach

Stealthy Attacks and Robust Detectors for Cyber-Physical Systems with Bounded Disturbances: A Zonotope Approach

Periodic Event-Triggered MPC for Continuous-Time Nonlinear Systems With Bounded Disturbances

This paper is concerned with periodic event-triggering laws in robust model predictive control (MPC) for continuous-time constrained nonlinear systems. The online optimal control problem solved at triggering times is introduced. A periodic static event-triggering condition, in which a fixed sampling time interval plays an important role in avoiding Zeno behavior, is presented to alleviate continuous checking of event detections. Then a periodic dynamic event-triggering condition is investigated to further enlarge the minimal inter-execution time. Single-mode MPC with a prediction horizon larger than the control one is considered. Sufficient conditions of recursive feasibility for the online optimal control problem are derived. In order to relax the sufficient condition of stability, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Ultimately Boundedness</i> properties are utilized in stability analysis. Finally, numerical simulation is provided to demonstrate the effectiveness of the proposed methods.

Ellipsoidal Set-Based Extended Command Governor for Constrained Linear Systems With Bounded Disturbances

The purposes of this paper are twofold. The first is to derive a convex formulation for optimizing the fictitious dynamics of the extended command governor strategy recently proposed in [1]. The second purpose is to provide an efficient procedure to solve online the optimization problem of the ellipsoidal set based command governor or the extended command governor. Two numerical examples with comparison to earlier solutions from the literature illustrate the effectiveness of the proposed algorithm.

Controlled Invariant Sets of Discrete-Time Linear Systems with Bounded Disturbances

This paper proposes two novel methods for computing the robustly controlled invariant set of linear discrete-time systems with additive bounded disturbances. In the proposed methods, the robustly controlled invariant set of discrete-time systems is obtained by solving the linear matrix inequality given by logarithmic norm and difference inequality. Illustrative examples are presented to demonstrate the obtained methods.

A New Adaptive Suboptimal Controller for a Class of Linear Discrete-Time Systems with Unknown Bounded Disturbances

This paper deals with adaptive suboptimal control of linear discrete-time, time-invariant, minimum phase, scalar systems in the presence of arbitrary bounded unmeasurable disturbances whose upper and lower bounds are a priori unknown. The distinguishing feature of the systems to be controlled is that there is no information concerning a priori knowledge of a bounded set to which the unknown parameters of these systems belong. Novelty of this paper is that, instead of unknown a priori membership set of parameters, the peculiar a posteriori membership sets are designed via the use of the measured signals. The adaptive suboptimal control algorithm utilizing this approach is proposed. The properties of the adaptive controller including the convergence of the adaptation procedure and also the ultimate boundedness of system's signals are established. To demonstrate an efficiency of this controller and support the theoretical study, simulation results are presented.

Hybrid Neural Network Control for Uncertain Nonlinear Discrete-Time Systems with Bounded Disturbance

Hybrid Neural Network Control for Uncertain Nonlinear Discrete-Time Systems with Bounded Disturbance

Quantized Impulsive Control of Linear Systems Under Bounded Disturbances and DoS Attacks

This article is concerned with the input-to-state stability (ISS) of linear systems with quantized state measurements under both external disturbances and denial-of-service attacks. Piecewise constant state quantizers taking a set of finite values are considered in this article. Depending on whether the bound of disturbances is known or not, two impulsive controllers that ensure ISS are designed. Leveraging the disturbance bound, the first controller can counteract the disturbances and guarantee that the quantizer never saturates at successful transmission instants. The second controller, which though cannot prevent the quantizer from saturation, is able to stabilize the system under disturbances whose bound is unknown, if the quantizer’s saturation duration is small enough. Moreover, analysis shows that with appropriate control parameter design, the resultant saturation duration always remains small. Finally, a numerical example is given to corroborate the practical merits of the proposed controllers and theory.

Analysis of an Extremum Seeking Controller Under Bounded Disturbance.

One of the applications of Extremum Seeking (ES) is to localize the source of a scalar field by using a mobile agent that can measure this field at its current location. While the scientific literature has presented many approaches to this problem, a formal analysis of the behavior of ES controllers for source seeking in the presence of disturbances is still lacking. This paper aims to fill this gap by analyzing a specific version of an ES control algorithm in the presence of source movement and measurement disturbances. We define an approximate version of this controller that captures the main features but allows for a simplified analysis and then formally characterize the convergence properties of this approximation. Through simulations and physical experiments, we compare the theoretically-predicted regions of attraction of the simplified system with the behavior of the full system and show that the simplified version is a good predictor of the behavior of the initial ES controller.

TS Fuzzy Robust Sampled-Data Control for Nonlinear Systems with Bounded Disturbances

We investigate robust fault-tolerant control pertaining to Takagi–Sugeno (TS) fuzzy nonlinear systems with bounded disturbances, actuator failures, and time delays. A new fault model based on a sampled-data scheme that is able to satisfy certain criteria in relation to actuator fault matrix is introduced. Specifically, we formulate a reliable controller with state feedback, such that the resulting closed-loop-fuzzy system is robust, asymptotically stable, and able to satisfy a prescribed H∞ performance constraint. Linear matrix inequality (LMI) together with a proper construction of the Lyapunov–Krasovskii functional is leveraged to derive delay-dependent sufficient conditions with respect to the existence of robust H∞ controller. It is straightforward to obtain the solution by using the MATLAB LMI toolbox. We demonstrate the effectiveness of the control law and less conservativeness of the results through two numerical simulations.

Scalable and Safe Multi-Agent Motion Planning with Nonlinear Dynamics and Bounded Disturbances

We present a scalable and effective multi-agent safe motion planner that enables a group of agents to move to their desired locations while avoiding collisions with obstacles and other agents, with the presence of rich obstacles, high-dimensional, nonlinear, nonholonomic dynamics, actuation limits, and disturbances. We address this problem by finding a piecewise linear path for each agent such that the actual trajectories following these paths are guaranteed to satisfy the reach-and-avoid requirement. We show that the spatial tracking error of the actual trajectories of the controlled agents can be pre-computed for any qualified path that considers the minimum duration of each path segment due to actuation limits. Using these bounds, we find a collision-free path for each agent by solving Mixed Integer-Linear Programs and coordinate agents by using the priority-based search. We demonstrate our method by benchmarking in 2D and 3D scenarios with ground vehicles and quadrotors, respectively, and show improvements over the solving time and the solution quality compared to two state-of-the-art multi-agent motion planners.

State Observers for Systems Subject to Bounded Disturbances Using Quadratic Boundedness

Quadratic boundedness is adopted to construct state observers for linear, piecewise linear, and Lipschitz nonlinear systems subject to bounded disturbances. Upper bounds on the estimation error are derived by exploiting quadratic boundedness and a design method based on linear matrix inequalities is proposed to minimize such bounds. Simulation results are provided to show the effectiveness of the proposed approach.

Extended Dissipative Control for Markovian Jump Time-Delayed Systems with Bounded Disturbances

In this work, the result of reachable set bounding and extended dissipative control synthesis of the Markovian jump time-delayed system is studied subject to stochastic actuator failures and partially known transition probabilities. Specifically, a novel actuator fault model is designed, in which the actuator fault matrix satisfies a certain probabilistic condition. Under the construction of an appropriate Lyapunov–Krasovskii functional (LKF), as well as reciprocal convex approach, Jensen’s integral inequality, and reachable set lemma, delay-dependent sufficient criteria are obtained in terms of linear matrix inequalities (LMIs) for finding an ellipsoid to bound the reachable sets of the Markovian jump time-delayed system with bounded disturbances. Finally, two numerical examples are provided to validate the effectiveness of the proposed strategy.

Error Bounds for PD-Controlled Mechanical Systems Under Bounded Disturbances Using Interval Arithmetic

We present a numerical algorithm based on invariant set theory to evaluate the worst-case performance of PD-controlled mechanical systems affected by bounded disturbances. By performing a specific coordinate transformation, the search and computation of positive invariant sets is simplified. It is shown that, thanks to the preservation of problem structure, the proposed method allows to obtain tight, component-wise bounds on the states, which are especially useful for performance evaluation and tuning of a PD controller. The bounds are formally guaranteed and can be used for safety certification. The method is compared to ultimate boundedness, and the superior results are shown via numerical simulations.

Adaptive Bipartite Consensus of Second-Order Multi-Agent Systems With Bounded Disturbances

This paper investigates distributed adaptive bipartite consensus for second-order multi-agent systems (MASs) with bounded disturbances under a signed graph. Based on adaptive variable structure control strategies, an adaptive bipartite consensus protocol is proposed, which guarantees that the bipartite consensus can be realized if the signed graph is structurally balanced and connected. Furthermore, the external disturbances are attenuated effectively by the variable structure control. And the obtained results are applied to adaptive consensus of disturbed second-order MASs under cooperative networks. Finally, a numerical simulation is presented to demonstrate the theoretical finding.

Robust adaptive unknown input observer design for a class of disturbed systems

This paper proposes a novel approach for designing a robust adaptive unknown input observer (UIO) for a class of nonlinear system. The system is composed of nonlinear terms and exogenous disturbance and fault signals which are considered to be unknown. The main contribution of the paper is to present the UIO system that uses adaptive law and linear matrix inequality (LMI). Adaptive law is used for system current fault estimation and LMI is used to provide the feasible set of responses while ensuring system stability. The effectiveness of the proposed method is shown by applying to the numerical examples. The simulation results show the validity of this method for a nonlinear system with unknown upper bound disturbance.

A Convexity Approach to Dynamic Output Feedback Robust MPC for LPV Systems with Bounded Disturbances

A convexity approach to dynamic output feedback robust model predictive control (OFRMPC) is proposed for linear parameter varying (LPV) systems with bounded disturbances. At each sampling time, the model parameters and disturbances are assumed to be unknown but bounded within pre-specified convex sets. Robust stability conditions on the augmented closed-loop system are derived using the techniques of robust positively invariant (RPI) set and the S-procedure. A convexity method reformulates the non-convex bilinear matrix inequalities (BMIs) problem as a convex optimization one such that the on-line computational burden is significantly reduced. The on-line optimized dynamic output feedback controller parameters steer the augmented states to converge within RPI sets and recursive feasibility of the optimization problem is guaranteed. Furthermore, bounds of the estimation error set are refreshed by updating the shape matrix of the future ellipsoidal estimation error set. The dynamic OFRMPC approach guarantees that the disturbance-free augmented closed-loop system (without consideration of disturbances) converges to the origin. In addition, when the system is subject to bounded disturbances, the augmented closed-loop system converges to a neighborhood of the origin. Two simulation examples are given to verify the effectiveness of the approach.

Stochastic Filtering of Max-Plus Linear Systems With Bounded Disturbances

The objective of this paper is to propose a filtering strategy for max-plus linear systems with bounded disturbances without the direct calculation of the a posteriori state probability. The strategy is based on the inversion of the expectation of the measure with respect to the state variable. Among the possible solutions, the closest to the prediction is chosen. An algorithm, based on interval propagation, is proposed to solve this problem. Simulations are performed to show the consistence of the proposed methodology with other approaches in the literature.

Problems of Adaptive Optimal Control of Discrete-Time Systems under Bounded Disturbance and Linear Performance Indexes

We present some problems of adaptive optimal robust control of linear discretetime systems under uncertainty and bounded external disturbance in which the optimal or guaranteed value of the performance index is a linear or linear-fractional function of unknown parameters of the system and set-membership estimation based on the method of recurrent objective inequalities reduces to recurrent updating of polyhedral estimates of unknown parameters. In such problems, computing current optimal estimates becomes a recurrent linear programming problem which is computationally tractable on modern computers for systems with a small number of estimated parameters.

Control Invariant Sets of Linear Systems with Bounded Disturbances

In this paper, algorithms to compute robust control invariant sets are proposed for linear continuous-time systems subject to additive but bounded disturbances. Robust control invariant sets of linear time invariant systems are achieved by logarithmic norm. Robust control invariant sets of linear uncertain systems, which are level sets of the storage functions, are obtained by solving functional differential inequality. Simulation shows that the proposed algorithms can yield improved minimal volume robust control invariant sets approximations in comparison with the schemes in the existing literature.

Control of Nonlinear Systems Subject to Amplitude Bounded Disturbances Using a N-fuzzy Strategy

Abstract The dynamic output feedback stabilization problem of nonlinear discrete-time systems subject to amplitude bounded disturbances by means of Takagi-Sugeno (T-S) N-fuzzy models is considered in this paper. The linear matrix inequality (LMI) approach is applied to design a dynamic output feedback fuzzy controller such that the system trajectories are ultimately bounded, that is, the state trajectory starting in a set of admissible initial conditions is guaranteed to converge in finite time to a nearby region of the state space origin. Furthermore, the proposed approach enables to handle with nonlinearities that are not function of the measured outputs but are sector bounded. A numerical example is considered to illustrate the effectiveness of the developed technique.