Tracking and Regulation in Linear Systems

Regulation of Linear Systems with Unknown Additive Sinusoidal Sensor Disturbances

We look at the stabilization and regulation problems for linear systems subject to both rate and saturation limits. With respect to stabilization we focus on semi-global stabilization. This allows one to use linear compensators. We concentrate on the state feedback, single-input case. However, the results can be extended to the measurement feedback and multi-input case.

This paper deals with the problem of robust tracking and disturbance rejection for a linear time-invariant system where the uncertainty of the system is represented in a structured form and the output to be controlled may be different from the measurement output. First, the problem is considered in a rather classical setting in that the required property of tracking and disturbance rejection can be attained as long as the resulting closed-loop system remains stable. Conditions for solvability of the problem are given and two algorithms are presented for designing controllers having the robust tracking and disturbance rejection property. Second, the problem of robust output regulation with robust stability is formulated as one of finding a controller such that the resulting closed-loop system satisfies an additional requirement of robust stability and thus the output regulation property can be maintained for all perturbations of uncertain parameters within a prescribed set. A procedure based on a high gain observer approach is proposed to solve this problem.

ABSTRACTIn this paper, we consider bipartite tracking of linear multi-agent systems with a leader. Both homogeneous and heterogeneous systems are investigated. The communication between agents is modelled by a directed signed graph, where the negative (positive) edges represent the antagonistic (cooperative) interactions among agents. Linear Quadratic Regulator (LQR)-based approach is used to derive the distributed protocol for the follower agent to achieve bipartite tracking of the leader. It is shown that solving the bipartite tracking problem over the structurally balanced signed graph is equivalent to solving the cooperative tracking problem over a corresponding graph with nonnegative edge weights. This bridges the gap between the newly raised bipartite tracking problem and the well-studied cooperative tracking problem. Three novel control protocols are proposed for both cooperative and bipartite output tracking of heterogeneous linear multi-agent systems. Numerical examples are given to show the effectiveness of our control protocols.

This paper addresses the event-triggered consensus tracking for general linear multi-agent systems with nonlinear uncertainty dynamics under directed communication topology. The proposed event-triggered consensus strategy relaxes the assumptions in existing works that the control gain and local inputs must be continuous. With the consensus tracking condition being satisfied, the cooperative control law with bounded parameter is developed based on the intermittent samples. It shows that if the sampling condition, in terms of LMIs, is satisfied, the resulting closed-loop general linear multi-agent uncertain systems will achieve the consensus. Simulation results are provided to verify the proposed approach.

Trajectory tracking and disturbance rejection for linear time-varying systems: Input/output representation

This paper is concerned with asymptotic tracking for linear systems with actuator saturation by output feedback control. Both reference inputs and disturbances are represented as zero-input responses of linear systems. The controller includes the internal model with an anti-windup term for the reference and disturbance signals and a state observer for the system to allow output feedback control. The overall system is shown to be asymptotically stable for any initial condition of the system as long as the magnitudes of the reference and disturbance signals are sized such that the asymptotic tracking of the reference signal can be achieved without saturating the actuator. A simulation example is presented to verify the effectiveness of the proposed approach.

Linear feedback control based on internal model principle achieves asymptotic tracking for linear system with known linear exogenous signal dynamics. This paper investigates the case of rejecting exogenous chaotic signals with known nonlinear dynamics for linear systems in the discrete time domain. Feedback controllers based on the internal model principle and predictive internal model control respectively are proposed and investigated in this paper. Both control algorithms are based on inversion of the linear system. It is shown that asymptotic tracking performance is achieved when perfect plant inversion is possible and it cannot be achieved with either algorithm when inversion errors from unmodeled dynamics or plant nonminimum phase zeros exist. The closed loop stability and performance rely on the relative size of the linear system inversion errors to the exogenous signal's local growth rate.

A spacecraft combined attitude and sun tracking system (CASTS) is a synergized system in which solar array drive assemblies are used as sun trackers and simultaneously as attitude control actuators. This paper, a continuous research on CASTS, addresses its attitude control problem. The kinematics and dynamics equations of a rigid spacecraft attitude motion is inherently nonlinear. In the attitude regulation problem, the attitude motion can be treated as a simple linear system for a constrained range of operating conditions, but it has impacts on the accuracy of the linear model when a model-based controller is implemented. Naturally, this is a compromise between simplicity and accuracy that all design engineers have to face. In this paper, we present a systematic approach to improve the accuracy while preserving the model as linear as possible, by deriving a quasi-linear approximation of a nonlinear spacecraft attitude motion. The quasi-linear approximation is based on the framework of the Takagi–Sugeno (T–S) fuzzy model. If a spacecraft can be modeled in the form of a rule-based T-S fuzzy system that acts as an interpolator between linear state-space systems, an approach called parallel distributed control (PDC) can be used to stabilize the attitude motion. The design philosophy of PDC is to create a simple fuzzy controller, where each rule’s consequent is a control law designed to stabilize the linear system in the corresponding consequent of the spacecraft T-S fuzzy system. Numerical results validate that the attitude and sun-tracking performances are achievable using the proposed PDC strategy.Â

In this paper, a H ∞ /Leitmann approach to the robust tracking control design is presented for an uncertain dynamic system. This new method is developed in the following two steps. Firstly, a tracking dynamic system with simultaneous consideration of parameter uncertainty and noise is modeled based on a linear system and a reference model. Accordingly, a “nominal system” from the tracking system is defined and controlled by a H ∞ control to obtain the asymptotical stability and noise resistance. Secondly, by making use of a Lyapunov function and the norm boundedness, a new robust control with the “Leitmann approach” is designed to cope with the uncertainty. The two controls collaborate with each other to achieve “uniform tracking boundedness” and “uniform ultimate tracking boundedness”. The new approach is then applied to an aircraft turbofan control design, and the numerical simulation results show the prescribed performances of the closed-loop system and the advantage of the developed approach.

As the minimal prototype control system has fast response,smaller overshoots and smaller stable errors,it is suitable for a photo-electric tracking system to capture targets.Therefore,this paper designs a minimal prototype control system for a photo-electric tracking frame and also performs simulation and experimental tests。The experiments show that the simulation results are coincident with that of experiments well,which not only demonstrates that the minimal prototype control system is a linear system in the certain region of tracking signal,but also indicates the influences of a correction part and a front filter.This control method reduces overshoot and adjusting time,inhibits the jitter effect of system.These all show that minimal prototype control method can be used to acquire fast targets in digital guiding and is valuable in the project application for opto-electronic tracking systems.

In this paper, a decentralized control scheme for group formation and trajectory tracking of multi-agent systems is designed. In this scheme, each agent dynamics is represented by a single-input single-output linear systemand the information that each controller requires is only the output of the others agents. With the proposed decentralized control law, multiagent system tracks asymptotically the trajectory and formation of the agents, even in the presence of smooth changes of formations. Moreover, the agent dynamics (structure and dimension) are not restricted to be the same, as usually assumed in the literature. A simulation example is provided in order to illustrate the application of the proposed control.

The current paper investigates design and analysis problems of formation tracking for high-order linear time-invariant swarm systems, where communication topologies among agents have leader-following structures and the whole energy supply is limited. Firstly, the communication topology of a swarm system is depicted by a directed graph with a spanning tree, where the communication channels from the leader to followers are directional and the communication channels among followers are bidirectional, and a new formation tracking protocol with an energy integral term and a given upper bound is proposed to achieve formation tracking with the limited energy. Then, sufficient conditions for time-varying formation tracking design and analysis with the limited energy are presented, respectively, which include two/three linear matrix inequality constraints associated with the maximum and minimum nonzero eigenvalues of the Laplacian matrix of a communication topology. Especially, time-invariant formation tracking criteria are further deduced. Finally, two numerical examples are revealed to verify main theoretical conclusions.

For linear time-varying single-input single-output systems, the paper treats the problem of designing an output feedback controller resulting in an (internally) stable closed-loop system that tracks a given reference signal. The design is accomplished by augmenting the given system to include an internal model of the reference signal. The internal model reduces to the usual form when the given plant is time invariant. An explicit construction for the internal model is given in the case of a step reference.

Formation-containment tracking for general linear multi-agent systems with a tracking-leader of unknown control input