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

In this paper we study the fundamental limitations in stabilization and tracking of multi-input, multi-output (MIMO) networked feedback systems. We adopt a parallel additive white noise (AWN) model for the MIMO communication channel, and consider as our performance measure the mean square error for a system's output to track a random reference signal with finite power. Of particular interest in our study is the joint design of the controller and the channel to mitigate the requirement on feedback stabilization and to better the tracking performance. To this effect we consider scaled AWN channels, with positive diagonal scaling matrices interpreted as static coders and decoders. By casting the problem as a constrained optimal H 2 control problem and employing duality principles, we derive necessary and sufficient conditions for the system to be mean-square stabilizable and analytical characterizations for the best achievable performance under channel input power constraint. While fundamental limits are known to exist, it is seen that an appropriate channel scaling can be employed to exploit the channel power effectively so as to fundamentally improve a system's stabilizability and tracking performance.

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.

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.

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.

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.

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

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.

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.

Optimal tracking performance of networked control systems under communication constraints

Existing control schemes for 5-DOF robotic manipulators suffer from fundamental limitations: conventional PID controllers cannot handle nonlinear dynamics and coupling effects, adaptive methods exhibit slow response to sudden parameter changes, robust H∞ controllers sacrifice performance for worst-case robustness, and intelligent methods lack formal stability guarantees. These limitations become critical in high-precision applications requiring simultaneous handling of model uncertainties, external disturbances, nonlinearities, and physical constraints. This paper addresses these challenges by proposing a novel integrated control architecture that systematically combines four complementary control methodologies within a unified framework: (1) adaptive H-infinity control providing formal robustness guarantees, (2) Model Predictive Control enabling constraint handling and optimization, (3) Fuzzy Logic control managing complex nonlinearities, and (4) Sliding Mode Control with enhanced disturbance observer for high-frequency noise rejection. The primary contribution is a novel adaptive weighting mechanism that dynamically adjusts each controller's contribution based on real-time performance metrics using exponential functions of tracking error magnitude, ensuring smooth transitions and optimal resource allocation without hard-switching limitations. The integrated framework employs a comprehensive mathematical analysis including composite Lyapunov stability proofs to guarantee asymptotic convergence of tracking error and boundedness of control signals. Rigorous theoretical analysis provides formal convergence guarantees and robustness bounds for parameter variations up to ±30%. The proposed approach is validated through extensive simulations conducted on MATLAB/Simulink using a detailed 5-DOF robotic manipulator model with clearly defined Denavit-Hartenberg parameters, mass distribution, and inertial properties. Simulation results demonstrate significant performance enhancement compared to conventional control methods. The proposed controller achieves superior tracking accuracy with RMS tracking error of 1.35 mm compared to 2.50 mm for H∞ control, 2.87 mm for adaptive control, and 5.58 mm for PD control, representing up to 46% improvement over the best existing robust control method. The system exhibits exceptional robustness with only 11.5% performance degradation under ±30% parameter variations compared to 31.2% degradation for H∞ control and 85.3% for PD control. Disturbance rejection capability is demonstrated with maximum tracking error of 3.21 mm and recovery time of 0.43 s under 5N external force disturbance, significantly outperforming conventional methods.

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.

A novel design technique for high performance drives employing both H/spl infin/ optimal control and fuzzy control is proposed in this paper. The fuzzy control design is equipped with an adaptive learning algorithm to achieve H/spl infin/ tracking performance with external disturbances. It gives elevation to the selection of optimal performance weights without any trial and error attempt. The idea is to establish a link between H/spl infin/ optimal control design and fuzzy control design, so as to provide H/spl infin/ tracking design with more intelligence and achieve better performance with fuzzy control design. The effect of both fuzzy logic approximation error and external disturbance on the tracking error is attenuated to an assigned level. The control strategy does not require explicit knowledge of the motor/load dynamics, which is a useful feature when dealing with parameter and load uncertainties. The robustness of the proposed methodology is displayed for different types of trajectories. Experimental and simulation results suggest that the effect of both the fuzzy approximation error and external disturbance on the tracking error can be attenuated efficiently by the H/spl infin/ adaptive fuzzy control. Accordingly, the proposed design method is suitable for the robust tracking control of the uncertain nonlinear drive systems and is an attractive control design philosophy. Test results obtained indicate excellent tracking performance for both speed and position. Test results illustrate the validity of the proposed approach.

In this paper, the design problem of delayed output feedback control scheme using two-layer interval fuzzy observers for a class of nonlinear systems with state and output delays is investigated. The Takagi-Sugeno type fuzzy linear model with an on-line update law is used to approximate the nonlinear system. Based on the fuzzy model, a two-layer interval fuzzy observer is used to reconstruct the system states according to equal interval output time delay slices. Subsequently, a delayed output feedback adaptive fuzzy controller is developed to override the nonlinearities, time delays, and external disturbances such that the H∞ tracking performance is achieved. The linguistic information is developped by setting the membership functions of the fuzzy logic system and the adaptation parameters to estimate the model uncertainties directly for using linear analytical results instead of estimating nonlinear system functions. The filtered tracking error dynamics are designed to satisfy the Strictly Positive Realness (SPR) condition. Based on the Lyapunov stability criterion and linear matrix inequalities (LMIs), some sufficient conditions are derived so that all states of the system are uniformly ultimately bounded and the effect of the external disturbances on the tracking error can be attenuated to any prescribed level and consequently an H∞ tracking control is achieved. Finally, a numerical example of a two-link robot manipulator is given to illustrate the effectiveness of the proposed control scheme.

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.

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.