Optimal tracking performance: preview control and exponential signals

SUMMARYThe optimal tracking problem for multiple‐input multiple‐output linear‐time‐invariant discrete‐time systems with communication constraints in the feedback path is studied in this paper. The tracking performance is measured by the energy of the error signal between the output of the plant and the reference signal. The objective is to obtain an optimal tracking performance, attainable by all possible stabilizing compensators. It is shown that the optimal tracking performance consists of two parts, one depends on the nonminimum phase zeros and zero direction of the given plant, as well as the reference input signal direction, and the other depends on the nonminimum phase zeros, unstable poles, and pole direction of the given plant, as well as the bandwidth and additive white Gaussian noise of the communication channel. It is also shown that, if the constraint of the communication channel does not exist, the optimal tracking performance reduces to the existing tracking performance of the control system without communication constraints. A typical example is given to illustrate the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.

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

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

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.

Optimal tracking performance of networked control systems under communication constraints

This paper proposes feedback control algorithms suitable for the top level of a hierarchical approach to controlling Flexible Manufacturing Systems (FMS). Preview and state feedback control techniques are employed to regulate the inventory levels near zero. The resulting controller utilizes inventory state feedback and anticipatory demand feedforward control, referred to as preview control. The preview control takes on the form of demand filtering. Special dynamic properties of the demand filter are discussed. We show how future demand information is related to present production and inventory levels. Production constraints are explicitly handled in the development of the feedback controller. We present numerical results for a test case.

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.

This paper has presented hard braking control system based on Adjustable Gain Enhanced Fuzzy Logic Controller (AGE-FLC) for optimal wheel slip ratio tracking performance. The purpose of the study was to improve slip ratio tracking and eliminate cycling while achieving very much shortened distance during emergency braking. The model of a braking vehicle at speed of 30 m.s^-1 subject to wheel locking was developed and implemented in MATLAB/Simulink environment. Simulation was conducted without a controller to study the slip ratio performance of the system on different road surfaces. The simulation results showed that stopping distance was 135.2 m in 5 seconds. A Fuzzy Logic Controller (FLC) whose control signal was enhanced by adding an adjustable gain mechanism to its output was designed. Simulation results showed that the AGE-FLC controller offered optimal tracking of desired wheel slip ratio of 0.1 as fast as possible on all road surface scenarios, while improving the stopping distance by 70.4% on dry road surface, 63.3% on wet road surface, 57.5% on cobblestone road surface and 48.8% on snow road surface in 2.651seconds.

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.

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.

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.

In this paper, we propose a practical robust fuzzy control design scheme that achieves optimal tracking performance and requires limited accuracy in the plant model. The plant is identified as a fuzzy combination of Takagi-Sugeno type linear models, and the fuzzy controller is optimized by genetic algorithms according to both the tracking performance and the attenuation level. The procedure applies the lately proposed idea of the fuzzy Lyapunov function that is less conservative then the traditional Lyapunov function candidate approach, and ensures H∞ robust tracking. The effectiveness of the proposed scheme is demonstrated by the fuzzy tracking control of an uncertain chaotic system with external disturbance.

The availability of predictions of future system inputs has motivated research into preview control to improve set-point tracking and disturbance rejection beyond that achievable via conventional feedback control. The design of preview controllers, typically based upon model predictive control (MPC) for its constraint handling properties, is often performed in a monolithic nature, coupling the feedback and feed-forward problems. This can create problems, such as: (i) an additional feedback loop is introduced by MPC, which alters the closed-loop dynamics of the existing feedback compensator, potentially resulting in a deterioration of the nominal sensitivities and robustness properties of an existing closed-loop and (ii) the default preview action from MPC can be poor, degrading the original feedback control performance. In our previous work, the former problem is addressed by presenting a modular MPC design on top of a given output-feedback controller, which retains the nominal closed-loop robustness and frequency-domain properties of the latter, despite the addition of the preview design. In this paper, we address the second problem; the preview compensator design in the modular MPC formulation. Specifically, we derive the key conditions that ensure, under a given closed-loop tuning, the preview compensator within the modular MPC formulation is systematic and well-designed in a sense that the preview control actions complement the existing feedback control law rather than opposing it. In addition, we also derive some important results, showing that the modular MPC can be implemented in a cascade over any given linear controllers and the proposed conditions hold, regardless of the observer design for the modular MPC. The key benefit of the modular MPC is that the preview control with constraint handling can be implemented without replacing the existing feedback controller. This is illustrated through some numerical examples.