Input Additive Disturbances Research Articles

Networked Control of a Small Drone Resilient to Cyber Attacks

With increasing advances in networked systems and networked control systems in everyday life, the problem of cybersecurity becomes crucial. Moreover, in some applications like small UAVs, the safety and integrity of the system and its surroundings are highly susceptible to cyberattacks. In this context, the current paper proposes a resilient networked control approach. The control structure is split into an inner and an outer loop. The outer position control loop uses measurements from motion cameras connected to a remote computer, while the commands are sent through the network. We consider the resilience problem for two types of cyberattacks: denial of service (DoS), emulated as an increase in the network transmission delay, and man in the middle (MitM), emulated as additive input disturbances. The mitigation for the DoS attack is performed through the help of a reference governor (RG), which uses the delay estimates and the system’s model to predict future safety violations and adapts the reference accordingly. The MitM attack is mitigated by an unknown input disturbance observer (UIDO) together with a RG. Experimental results on a Parrot Mambo drone show that both types of attacks are rejected successfully, ensuring a safe and stable flight.

Robust Action Governor for Discrete-Time Piecewise Affine Systems With Additive Disturbances

In this letter, we introduce an extension of the Action Governor (AG), which is an add-on, supervisory scheme to a nominal control loop to enforce safety-related requirements. This extension enables AG design based on discrete-time piecewise affine (PWA) system models with additive set-bounded disturbance inputs and non-convex exclusion-zone avoidance constraints. We establish theoretical properties and computational approaches for this robust version of AG, and illustrate its application to an autonomous vehicle control problem.

Bounded control of multiple oscillators system by using state-dependent saturation functions

This paper is concerned with the global stabilisation problem of multiple oscillators system with bounded controls by constructing state-dependent saturation functions. First, two types of planar systems subject to input additive disturbances are respectively stabilised by bounded feedbacks whose formulas involve state-dependent saturation function. Next, these results are used to stabilise multiple oscillators system of arbitrary length with bounded control based on a special canonical form. Explicit conditions are provided to guarantee the stability of the closed-loop system. Compared with the existing results, the proposed controllers contain the so-called state-dependent saturation functions and thus can improve the control performance significantly. Moreover, the corresponding results for the discrete-time case are also established. Two numerical examples are given to show the effectiveness and superiority of the proposed approaches.

Model predictive control paradigms for fish growth reference tracking in precision aquaculture

In precision aquaculture, the primary goal is to maximize biomass production while minimizing production costs. This objective can be achieved by optimizing factors that have a strong influence on fish growth, such as feeding rate, temperature, and dissolved oxygen. This paper provides a comparative study of four model predictive control (MPC) strategies for fish growth reference tracking under a representative bioenergetic growth model in precision aquaculture. We propose to evaluate four candidate MPC formulations for fish growth reference tracking based on the receding horizon. The first MPC formulation tracks a desired fish growth trajectory while penalizing the feed ration, temperature, and dissolved oxygen. The second MPC optimization strategy directly optimizes the feed conversion ratio (FCR), which is the ratio between food quantity and fish weight gain at each sampling time. This FCR-like optimization strategy minimizes the feed while maximizing the predicted growth state’s deviation from the given reference growth trajectory. The third MPC formulation includes a tradeoff between the growth rate trajectory tracking, the dynamic energy, and food cost. The last MPC formulation aims to maximize the fish growth rate while minimizing the costs. Numerical simulations that integrate a realistic bioenergetic fish growth model of Nile tilapia (Oreochromis niloticus) are illustrated to examine the comparative performance of the four proposed optimal control strategies. A sensitivity analysis is conducted to study the robustness of these MPC strategies with respect to the effect of the prediction horizon, the regularization term, and the additive input disturbances to the process. The obtained results show great potential and flexibility to meet the fish farmers’ needs depending on the type of fish, selling price, culture duration, and feed cost.

Observer-based semi-global containment of saturated multi-agent systems with uncertainties

In this article, the robust semi-global containment control for multi-agent systems affected by uncertainties, such as input additive disturbance, input saturation and dead zone is addressed. An observer-based control algorithm is designed by combining the high-gain observer approach and the low-and-high gain feedback technique. Under the assumption that all agents are asymptotically null controllable with bounded controls and each follower can access the information of at least one leader through a directed path, sufficient conditions for the semi-global output feedback containment control are provided. Finally, numerical simulations are proposed to verify the main theoretical results.

Global Stabilization of the Discrete-Time Integrators System by Bounded Controls

This paper is concerned with global stabilization of discrete-time multiple integrators with bounded controls by utilizing the energy function based approach. First, a discrete-time double integrators system subject to input additive disturbances is stabilized by a bounded feedback whose formula involves a linear function of the state and a saturation function only. Next, this result is used to stabilize a discrete-time multiple integrators of arbitrary length by bounded control with the aid of a special canonical form. Compared with the existing results, the proposed controllers require fewer saturation functions, which allow a better use of the control energy. Moreover, some free parameters that are introduced into these controllers can help improve the transient performance of the closed-loop systems significantly. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Aerial Slung-Load Position Tracking Under Unknown Wind Forces

We propose a dynamic controller for position tracking of a point-mass load attached to an omnidirectional aerial vehicle by means of a cable. Both the load and the aerial vehicle are subject to unknown wind forces. We model the dynamics of the slung-load system and put it into canonical form, i.e., a form which is independent of the system's physical parameters. Following a backstepping strategy, we design a dynamic control law for the canonical system that contains four estimators, since each of the two wind disturbances has two separate effects: an effect on the linear acceleration and another on the angular acceleration. Loosely speaking, the difference between the wind forces is an input-additive disturbance, while the wind force on the load is not, which makes removing the wind force on the load nontrivial. We identify conditions on the desired position trajectory and on the wind on the load, which guarantee that a well-defined equilibrium trajectory exists. The designed controller guarantees simultaneously that the latter trajectory is asymptotically tracked and the cable remains taut, provided that the system is initialized in a suitable set. Simulations illustrate our results.

A NARX Model Reference Adaptive Control Scheme: Improved Disturbance Rejection Fractional-Order PID Control of an Experimental Magnetic Levitation System

Real control systems require robust control performance to deal with unpredictable and altering operating conditions of real-world systems. Improvement of disturbance rejection control performance should be considered as one of the essential control objectives in practical control system design tasks. This study presents a multi-loop Model Reference Adaptive Control (MRAC) scheme that leverages a nonlinear autoregressive neural network with external inputs (NARX) model in as the reference model. Authors observed that the performance of multi-loop MRAC-fractional-order proportional integral derivative (FOPID) control with MIT rule largely depends on the capability of the reference model to represent leading closed-loop dynamics of the experimental ML system. As such, the NARX model is used to represent disturbance-free dynamical behavior of PID control loop. It is remarkable that the obtained reference model is independent of the tuning of other control loops in the control system. The multi-loop MRAC-FOPID control structure detects impacts of disturbance incidents on control performance of the closed-loop FOPID control system and adapts the response of the FOPID control system to reduce the negative effects of the additive input disturbance. This multi-loop control structure deploys two specialized control loops: an inner loop, which is the closed-loop FOPID control system for stability and set-point control, and an outer loop, which involves a NARX reference model and an MIT rule to increase the adaptation ability of the system. Thus, the two-loop MRAC structure allows improvement of disturbance rejection performance without deteriorating precise set-point control and stability characteristics of the FOPID control loop. This is an important benefit of this control structure. To demonstrate disturbance rejection performance improvements of the proposed multi-loop MRAC-FOPID control with NARX model, an experimental study is conducted for disturbance rejection control of magnetic levitation test setup in the laboratory. Simulation and experimental results indicate an improvement of disturbance rejection performance.

ISS of predictor feedback for multi-input affine nonlinear systems with distinct input delays

We develop a predictor feedback control scheme for multi-input affine nonlinear systems with distinct input delays in each individual input channel and additive disturbances. The input-to-state stable control Lyapunov function (ISS-CLF) is used to design control laws for the delay-free affine nonlinear systems. Then, a predictor-feedback controller is constructed for this class of nonlinear systems with input delays. We establish input-to-state stability with respect to additive plant disturbances, as well as we show that the control law derives gain margin guarantees. Our proofs are based on the infinite-dimensional backstepping transformation and the construction of a Lyapunov functional. The developed method is applied to the control of vehicular traffic flow at distant bottlenecks.

Exponential input-to-state stabilization of a class of diagonal boundary control systems with delay boundary control

This paper deals with the exponential input-to-state stabilization with respect to boundary disturbances of a class of diagonal infinite-dimensional systems via delay boundary control. The considered input delays are uncertain and time-varying. The proposed control strategy consists of a constant-delay predictor feedback controller designed on a truncated finite-dimensional model capturing the unstable modes of the original infinite-dimensional system. We show that the resulting closed-loop system is exponentially input-to-state stable with fading memory of both additive boundary input perturbations and disturbances in the computation of the predictor feedback.

Robust backstepping control of uncertain nonlinear systems with unknown time-varying input delay

A robust compensator is developed for a class of strict-feedback uncertain nonlinear systems with additive disturbance and unknown time-varying input delay. The compensator is composed of a Proportional-Integral (PI) control and delay compensation term based on a finite integral of the past control values. The sufficient inequality conditions on controller gains and upper bound of input delay are derived using a Lyapunov-based stability analysis by choosing suitable L-K functionals, which guarantee a global uniformly ultimately bounded (GUUB) tracking result. Simulation results show the performance and robustness of controller for different values of time-varying input delay.

Shrinking horizon parametrized predictive control with application to energy-efficient train operation

A nonlinear model predictive control approach is studied, for problems where a fixed terminal instant and corresponding terminal set to be reached are imposed. The new technique features a shrinking horizon, rather than the most common receding one, and an input parametrization strategy to reduce computational burden. The property of transferability of the parametrization strategy is introduced. Under this property, theoretical convergence guarantees in nominal conditions are obtained by construction. Two relaxed techniques are then proposed to retain recursive feasibility in presence of bounded additive input disturbance. A bound on the constraint violation achieved by these relaxed techniques as a function of the uncertainty bound is derived, too. The developed strategy is applied to the problem of energy-efficient operation of trains, in either a fully autonomous mode (with continuous input values) or a driver assistance mode (with discrete input values, resulting in a nonlinear integer program if no parametrization is used). Realistic simulation results in this context illustrate the effectiveness of the approach.

Lag‐bipartite consensus of linear multiagent systems under saturating input over signed graph

The objective of this study is to investigate lag-bipartite consensus of linear multiagent systems under saturating input with dead-zone constraint where two separate groups of follower agents reach the modulus of the leader state, but of opposite sign with a certain delay. The leader–follower bipartite consensus problem of saturating input with dead-zone is considered with the input signals of the followers being subjected to leader-influenced input additive uncertainties and disturbances. It is shown that if the agents interacting with each-other over the structurally balanced undirected graph having a directed spanning tree rooted at the leader are asymptotically null controllable with bounded controls, then the two proposed control laws – (i) a low-high gain based control law and (ii) a low-gain based variable-structure continuous tracking control law, can achieve lag-bipartite consensus as long as the initial conditions of all the agents remain within a priori bounded set. The numerical simulations establish the effectiveness of the theoretical results.

Robust global consensus tracking of linear multi‐agent systems with input saturation via scheduled low‐and‐high gain feedback

This study deals with the protocol design for achieving robust global consensus tracking of multi-agent systems. Agent dynamics are described as general linear systems with actuator saturation and input additive uncertainties and disturbances. Via developing a scheduled low-and-high gain design technique, the state feedback protocol is proposed, under which global consensus tracking and disturbance rejection for such systems can be achieved under the mild assumptions on agent dynamics and network topology. This result is further extended to the case of the reduced-order observer-based protocol design, with the help of the special coordinate basis approach. Finally, the advantages of the proposed protocols are illustrated by a numerical simulation.

Robust Semiglobal Coordination of Coupled Harmonic Oscillator Systems Subject to Input Saturation

In this paper, we investigate the problems of robust semiglobal coordination of coupled harmonic oscillator systems with input saturation together with dead zone and input additive disturbances, in which the coupled harmonic oscillators can serve as an approximation of modern complex systems in the field of system engineering, such as SoS (system of systems). By virtue of the parameterized low-and-high-gain feedback technique, sufficient conditions are provided to guarantee the robust semiglobal coordination of coupled harmonic oscillator systems with input saturation together with decentralized state-dependent input additive disturbances and distributed state-dependent input additive disturbances. Finally, numerical examples are proposed to verify all the theoretical results.

Robust Semi-Global Leaderless Consensus and Containment Control of Identical Linear Systems with Imperfect Actuators

This paper investigates both the robust semi-global leaderless consensus problem and the robust semi-global containment control problem for a group of identical linear systems with imperfect actuators. The imperfect actuators are characterized by nonlinearities such as saturation and dead zone and there input output relationships are not precisely known. The dynamics of follower agents are also affected by the input additive disturbances. Low-and-high gain feedback consensus protocols are constructed to solve these problems. More specifically, it is shown that robust semi-global leaderless consensus can be achieved over a connected undirected graph and robust semi-global containment control can be achieved when each follower agent has access to the information of at least one leader agent. Numerical simulation illustrates the theoretical results.

Inverse optimal design of input-to-state stabilisation for affine nonlinear systems with input delays

ABSTRACTWe establish robustness of the predictor feedback control law to perturbations appearing at the system input for affine nonlinear systems with time-varying input delay and additive disturbances. Furthermore, it is shown that it is inverse optimal with respect to a differential game problem. All of the stability and inverse optimality proofs are based on the infinite-dimensional backstepping transformation and an appropriate Lyapunov functional. A single-link manipulator subject to input delays and disturbances is given to illustrate the validity of the proposed method.

Detection of Attacks Against Power Grid Sensors Using Kalman Filter and Statistical Decision Making

A systematic method for the detection of attacks against sensors of the power grid is developed using Kalman filtering and statistical decision making criteria. The Kalman filter is used as a virtual sensor that emulates the functioning of the grid’s sensors in the fault-free mode. The output of the Kalman filter is compared against the output of the real sensors and the resulting differences generate the residuals’ sequence. The square of the residuals’ vector, weighted by the inverse of the associated covariance matrix is a random variable that follows the $\chi ^{2}$ distribution. This variable can serve as a statistical test about the deviation of the sensors functioning from the normal mode. By exploiting the properties of the $\chi ^{2}$ distribution and by using the confidence intervals approach, one can define thresholds against which the value of the statistical test is compared. If these thresholds are exceeded by the value of the statistical test, then it can be inferred that the sensors’ functioning is abnormal. By applying the statistical test on clusters of sensors, one can find sections of the power grid, which have been exposed to the attack. In addition, by applying the statistical test at each individual sensor, one can isolate the compromised sensors. Finally, by redesigning the Kalman filter as a disturbance observer, it is possible to estimate the additive disturbance inputs that affect the sensors. This information may indicate whether the deviation of the sensors functioning from normal has been the result of an attack to the grid by intruders.

Robust Semi-global Coordinated Tracking of Saturated Networked Systems

This paper focuses on the robust semi-global coordinated tracking of general linear systems subject to input saturation together with input additive disturbance and dead zone. A fully distributed algorithm which relating only with the number of the following agents and the relative state information of its neighbors is first constructed, and then sufficient conditions guaranteeing the robust semi-global consensus tracking and the robust semi-global swarm tracking are provided, respectively, on the basis of the low-and-high feedback technique. Finally, numerical simulations are performed to illustrate the effectiveness of the theoretical results.

Observer-Based Robust Coordinated Control of Multiagent Systems With Input Saturation.

This paper addresses the robust semiglobal coordinated control of multiple-input multiple-output multiagent systems with input saturation together with dead zone and input additive disturbance. Observer-based coordinated control protocol is constructed, by combining the parameterized low-and-high-gain feedback technique and the high-gain observer design approach. It is shown that, under some mild assumptions on agents' intrinsic dynamics, the robust semiglobal consensus or robust semiglobal swarm can be approached for undirected connected multiagent systems. Then, specific guidelines on the selection of the low-gain parameter, the high-gain parameter, and the high-gain observer gain have been provided. At last, numerical simulations are presented to illustrate the theoretical results.