Optimal tracking performance of MIMO discrete‐time systems with communication constraints

This paper studies optimal tracking performance issues for multi-input-multi-output linear time-invariant systems under networked control with limited bandwidth and additive colored white Gaussian noise channel. The tracking performance is measured by control input energy and the energy of the error signal between the output of the system and the reference signal with respect to a Brownian motion random process. This paper focuses on two kinds of network parameters, the basic network parameter-bandwidth and the additive colored white Gaussian noise, and studies the tracking performance limitation problem. The best attainable tracking performance is obtained, and the impact of limited bandwidth and additive colored white Gaussian noise of the communication channel on the attainable tracking performance is revealed. It is shown that the optimal tracking performance depends on nonminimum phase zeros, gain at all frequencies and their directions unitary vector of the given plant, as well as the limited bandwidth and additive colored white Gaussian noise of the communication channel. The simulation results are finally given to illustrate the theoretical results.

Optimal tracking performance of networked control systems under communication constraints

Optimal performance of discrete-time control systems based on network-induced delay

The analysis method of optimal tracking performance is proposed for multiple‐input multiple‐output (MIMO) linear time‐invariant (LTI) systems under disturbance rejection. AnH2criterion of the error signal between the output of the plant and the reference signal is used as a measure for the tracking performance. Spectral factorization is applied to obtain the optimal solution of the system tracking error. The explicit expressions are derived for this minimal tracking error with respect to random reference signals under disturbance rejection. It is shown that the nonminimum phase zeros, the zero direction, the unstable poles, the pole direction of a given plant, statistical characteristics of the reference input signal, and disturbance signal have a negative effect on a feedback system's ability to reduce the system error with disturbance rejection. The results show that the optimal tracking performance will further be damaged because of disturbance rejection. Some typical examples are given to illustrate the theoretical results.

This paper studies the optimal reference tracking problems of finite-dimensional, linear, time-invariant (LTI) systems with an additive white Gaussian noise (AWGN) channel between the controller and the plant. We consider two types of the reference signal: a random variable and a Brownian motion. The power of the tracking error is adopted as the measure of the performance and is to be minimized over all stabilizing two-parameter controllers. We assume the power of the channel input is limited and seek to solve the constrained optimization problem explicitly. It is shown that, besides the power constraint, the lowest power of the tracking error hinges closely on non-minimum phase zeros, the unstable poles and the plant gain.

Performance limitations in the tracking and regulation problem for discrete-time systems

We study tracking performance limitation problems. Two issues are addressed concerning how earlier results developed elsewhere may be extended to more general classes of reference signals, and how tracking performance may be further improved beyond that offered by feedback control. Toward these issues we consider exponentially increasing reference inputs and examine the use of preview control for tracking. Using an optimal interpolation approach, we develop analytical expressions and a conceptual insight which will aid in the understanding of these issues. To this effect, we derive explicit expressions for the optimal tracking error, either as exact solutions or bounds. It is found that for the exponential signals the earlier results can be directly extended, and similar conclusive statements can be drawn. It is also shown that, in general, preview can be used to advantage for improving tracking performance, especially in dealing with the effect resulted from plant nonminimum phase zeros.

This study investigates the tracking performance of continuous-time, multi-input multi-output, linear time-invariant systems in which the output feedback is subject to an additive white Gaussian noise corruption. The problem under consideration amounts to determining the minimal error in tracking a Brownian motion random process, which emulates a step reference signal in the deterministic setting. The authors consider both the unity feedback and two-parameter control structure. In the former case, they derive an explicit bound, and in the latter an exact expression of the minimal tracking error attainable under the noise effect. Both results demonstrate how the additive white Gaussian noise may degenerate the tracking performance, and how the noise effect may intertwine with unstable poles and non-minimum phase zeros which are intrinsic characteristics of the plant.

Under harsh geographical conditions where manned flight is not possible, the ability of the unmanned aerial vehicle (UAV) to successfully carry out the payload hold–release mission by avoiding obstacles depends on the optimal path planning and tracking performance of the UAV. The ability of the UAV to plan and track the path with minimum energy and time consumption is possible by using the flight parameters. This study performs the optimum path planning and tracking using Harris hawk optimization (HHO)–grey wolf optimization (GWO), a hybrid metaheuristic optimization algorithm, to enable the UAV to actualize the payload hold–release mission avoiding obstacles. In the study, the hybrid HHO–GWO algorithm, which stands out with its avoidance of local minima and speed convergence, is used to successfully obtain the feasible and effective path. In addition, the effect of the mass change uncertainty of the UAV on optimal path planning and tracking performance is determined. The effectiveness of the proposed approach is tested by comparing it with the metaheuristic swarm optimization algorithms such as particle swarm optimization (PSO) and GWO. The experimental results obtained indicate that the proposed algorithm generates a fast and safe optimal path without becoming stuck with local minima, and the quadcopter tracks the generated path with minimum energy and time consumption.

In this paper, we study optimal LQG tracking control problems for linear continuous-time hybrid systems. We adopt an approach to prepare some candidates of mode distributions and minimize value functions at each time for the systems and performance indices. By the approach, system states and mode distributions are simultaneously optimized so that the performance indices are minimized for available information of reference signals. We consider optimization problems for averaged systems and averaged performance indices throughout mode distributions. Finally we give numerical examples and verify that we can obtain both optimal tracking performance and optimal candidate of mode distributions by the algorithm presented in this paper.

We first present a formulation for the real-time tracking of a scalar continuous-time linear process over an Additive White Gaussian Noise (AWGN) channel without channel feedback and prove several results for minimum mean-squared error (MMSE) tracking. For the one-to-one channel case, we give an optimal encoder-decoder pair along with the optimal tracking performance. With the Gaussian distributed source innovation, one optimal form of the encoder is shown to be a linear innovation encoder, which scales the source innovation to match with the power constraint of the channel input. We then extend the formulation to the case where multiple source processes are tracked via a shared AWGN channel.

In this study, the optimal tracking performance for single-input multiple-output (SIMO) systems under control energy constraints is investigated. The packet dropouts in the upstream channel and down channel are adequately considered. The minimal tracking error is obtained by searching through all stablising controllers. The main results of this study show that the optimal tracking performance in these kinds of system is closely dependent on the structure of the given plant and statistic characteristics of the reference signal. Furthermore, the packet dropouts in the communication channel will degenerate the tracking performance. Finally, a typical example is given to illustrate the theoretical results.

In this paper, we consider the tracking of multiple targets in the presence of clutter with poorly localized sensors in multistatic sensor networks. In multistatic sensor networks, we have a few active sensors that emit the signals and many passive sensors that receive the signals originated from the active sensors and reflected by the targets and clutter. In anti-submarine warfare, sensors are typically deployed from aircraft. Optimal tracking performance can be achieved if all the sensor locations are known. However, in general, sensor deployment accuracy is poor, and sensors can also drift significantly over time. Hence, the location uncertainties will increase with time. If the sensors have global position system (GPS) receiver, then their locations can be located with reasonable accuracy. However, most of the cheap sensors do not have a GPS, and therefor, location uncertainties must be taken in to consideration while tracking. An advantage of multistatic sensors compared to independent monostatic sensors is that the sensors can also be tracked accurately. In this paper, we propose how to improve the tracking performance of multiple targets by incorporating sensor uncertainties. We obtain a bound on the tracking performance with location uncertainties being taken into consideration, and propose a technique to select a subset of sensors (if only a few of the available sensors can be used at any measurement time) that should be used at each time step based on the bound. Simulation results illustrating the performance of the proposed algorithms are also presented.

Cooperative vehicle safety systems (CVSSs) rely on vehicular networking for broadcasting state information in order to track neighbors’ positions and, therefore, to predict potential collisions. In vehicular networking, a large number of vehicles compete for access to the limited channel resource, causing channel congestion. The vehicle tracking accuracy, which is the basis for CVSSs, therefore, can be heavily affected. Moreover, the available channel resources must be shared among vehicles in a fair way in order to maintain accurate tracking accuracy for each vehicle. To realize fair access to channel resources while maintaining an accurate tracking performance under conditions of dynamic vehicle density, in this paper, we present a distributed fair transmission rate control strategy, based on multi-agent model predictive control (MPC). We first propose a dynamic information dissemination rate model to capture the state information dissemination ability under conditions of dynamic vehicle density. Then, we present a multi-agent information dissemination model, in which each vehicle is controlled by a control agent that uses MPC and coordinates with its neighboring agents in order to determine its optimal transmission rate actions. We then design an augmented-Lagrangian-based distributed decision-making scheme to find the optimal transmission rate actions and, at the same time, reach an agreement on fair and efficient channel utilization among the vehicles. Simulation results confirm that the distributed transmission rate control strategy can guarantee fair access to channel resources while achieving the optimal vehicle tracking performance under conditions of dynamic vehicle density.

This paper concerns the stabilization of linear time-invariant (LTI) systems subject to uncertain, possibly time-varying delays. The fundamental issue under investigation, referred to as the delay margin problem, addresses the question: What is the largest range of delay such that there exists a single LTI feedback controller capable of stabilizing all the plants for delays within that range? Drawing upon analytic interpolation and rational approximation techniques, we derive fundamental bounds on the delay margin, within which the delay plant is guaranteed to be stabilizable by a certain LTI output feedback controller. Our contribution is threefold. First, for single-input single-output (SISO) systems with an arbitrary number of plant unstable poles and nonminimum phase zeros, we provide an explicit, computationally efficient bound on the delay margin, which requires computing only the largest real eigenvalue of a constant matrix. Second, for multi-input multi-output (MIMO) systems, we show that estimates on the variation ranges of multiple delays can be obtained by solving LMI problems, and further, by finding bounds on the radius of delay variations. Third, we show that these bounds and estimates can be extended to systems subject to time-varying delays. When specialized to more specific cases, e.g., to plants with one unstable pole but possibly multiple nonminimum phase zeros, our results give rise to analytical expressions exhibiting explicit dependence of the bounds and estimates on the pole and zeros, thus demonstrating how fundamentally unstable poles and nonminimum phase zeros may limit the range of delays over which a plant can be stabilized by a LTI controller.