Optimal Tracking Error Research Articles

Robust nonlinear MPC without terminal constraint for tracking changing setpoints in the presence of non‐additive unknown disturbance

AbstractThis paper develops a novel robust tracking model predictive control (MPC) without terminal constraint for discrete‐time nonlinear systems capable to deal with changing setpoints and unknown non‐additive bounded disturbances. The MPC scheme without terminal constraint avoids difficult computations for the terminal region and is thus simpler to design and implement. However, the existence of disturbances and/or sudden changes in a setpoint may lead to feasibility and stability issues in this method. In contrast to previous works that considered changing setpoints and/or additive slowly varying disturbance, the proposed method is able to deal with changing setpoints and non‐additive non‐slowly varying disturbance. The key idea is the addition of tightened input and state (tracking error) constraints as new constraints to the tracking MPC scheme without terminal constraints based on artificial references. In the proposed method, the optimal tracking error converges asymptotically to the invariant set for tracking, and the perturbed system tracking error remains in a variable size tube around the optimal tracking error. Closed‐loop input‐to‐state stability and recursive feasibility of the optimization problem for any piece‐wise constant setpoint and non‐additive disturbance are guaranteed by tightening input and state constraints as well as weighting the terminal cost function by an appropriate stabilizing weighting factor. The simulation results of the satellite attitude control system are provided to demonstrate the efficiency of the proposed predictive controller.

Online adaptive optimal tracking control for model-free nonlinear systems via a dynamic neural network

This paper presents an online adaptive approximate solution for the optimal tracking control problem of model-free nonlinear systems. Firstly, a dynamic neural network identifier with properly designed weights updating laws is developed to identify the unknown dynamics. Then an adaptive optimal tracking control policy consisting of two terms is proposed, i.e. a steady-state control term is established to ensure the desired tracking performance at the steady state, and an optimal control term is proposed to ensure the optimal tracking error dynamics optimally. The composite Lyapunov method is used to analyse the stability of the closed-loop system. Two simulation examples are presented to demonstrate the effectiveness of the proposed method.

스마트 베타 전략에 따른 액티브 주식형 펀드의 최적 추적오차

Purpose - This study introduces a methodology for finding the optimal tracking error of active stock funds. Tracking error is commonly used in risk budgeting techniques as a concept of cost for alpha creation.
 Design/methodology/approach - This study uses a post-optimal smart beta portfolio that maximizes alpha under the given tracking error constraint.
 Findings - As a result of the analysis, the smart beta strategy that maximized alpha under the constraint of 0.15% daily tracking error shows the highest IR. This means the maximum theoretically achievable efficiency. In this regard, a fixed-effect panel regression analysis is conducted to evaluate the active efficiency of domestic stock funds. In addition to control variables based on previous studies, the effect of tracking error on alpha is analyzed. The alpha used in this model is calculated using the smart beta portfolio according to the size of the constraint of the tracking error as a benchmark. Contrary to theoretical estimates, in Korea, the alpha performance is maximized under a daily tracking error of 0.1%. This indicates that the active efficiency of domestic equity funds is lower than the theoretical maximum.
 Research implications or Originality - Based on this study, it is expected that it can be used for active risk management of pension funds and performance evaluation of active strategies.

Robust MPC for tracking changing setpoints in discrete‐time non‐linear systems with non‐additive unknown disturbance

This paper develops a novel observer-based robust tracking predictive controller for discrete-time nonlinear affine systems capable of dealing with changing setpoints and non-additive non-slowly varying unknown disturbance with bounded variations. The existence of disturbance and/or sudden changes in a setpoint may lead to feasibility and stability issues in the stabilizing terminal constraint-based MPC. Since robust tracking MPCs usually consider additive disturbance, the recursive feasibility of these methods may be lost in the presence of non-additive non-slowly varying disturbance. The robust tracking MPC presented here extends the artificial reference-based MPC to deal with both changing setpoints and non-additive non-slowly varying disturbance. The key idea is the addition of tightened input and state constraints as new system constraints. The authors also guarantee the boundedness of disturbance observation error and closed-loop tracking error. In this method, the optimal tracking error converges asymptotically to the terminal region, and the perturbed system tracking error remains in a variable size tube around the optimal tracking error. It is shown that the proposed controller can achieve offset-free tracking in the presence of constant disturbance. The simulation results of the satellite attitude control system are provided to demonstrate the efficiency of the proposed predictive controller.

Intent-Aware Optimal Collision Avoidance and Trajectory Planning for a Pursuit Vehicle

SummaryThis paper presents an integrated optimal control framework for velocity and steering control of an autonomous pursuit vehicle, where the control objectives satisfy the requirements of collision avoidance and moving target tracking. A distinctive feature of the proposed velocity and steering control is the application of logarithmic penalty functions to both. The control barrier imposed by logarithmic function provides a unique tool in computing a balanced trajectory with optimal tracking error, control effort and safety margin. Trajectories compliant with the safety regulations for autonomous driving have been planned based on estimated intention of the target and the obstacles. Effects of the controller weights have been extensively simulated to assess the performance of the proposed strategy in a variety of dynamic situations. The controller has been validated on a real-life robot by using a shrinking horizon control policy for iterative optimisation.

Analysis of optimal performance of MIMO networked control systems with encoding and packet dropout constraints

In this study, optimal performance of the multi-input multi-output networked control systems (NCSs) is analysed. The systems are with a time-delay and channel noise constraints in the forward network channel, and encoding-decoding and quantisation constraints, and packet dropouts in the feedback network channel. By using the Youla parameterisation of a two-degree-of-freedom controller, a new and explicit expression of the optimal performance is derived. The optimal performance is obtained using the method of H 2 norm technique. The results show that the positions and directions of the non-minimum phase zeros and unstable poles of a given plant are related to the optimal tracking error. On the other hand, the optimal tracking error is dependent on channel noise, quantisation noise, encoding-decoding, time-delay, packet dropout probability and other correction factors. Finally, simulation results demonstrate the effectiveness of the proposed control scheme.

Tracking Unstable Autoregressive Sources Over Discrete Memoryless Channels

We consider the problem of tracking, in realtime, an unstable autoregressive (AR) source over a discrete memoryless channel (DMC). We present computable achievable bounds on the optimal tracking error for general DMCs, and we particularize these bounds to the binary erasure, packet erasure, and binary symmetric channels. The achievable bounds in this paper are proved using a partially separate source quantization and channel coding architecture. We do not use complete or strict separation in usual Shannon sense: 1) the quantiser’s resolution is optimized against the error-correction capabilities of the channel code and the channel code is optimized against an AR Hamming distortion function matched to the source (a weighted Hamming distortion function that provides unequal error protection to different parts of the AR source). The achievability results for general DMCs are proved by combining the AR Hamming distortion function with new realtime (streaming) versions of the random coding union and dependence testing bounds . When applied to erasure channels, these general bounds combine with simple converses to demonstrate that the channel’s cutoff rate plays an important role in realtime tracking.

MASALAH GALAT PENJEJAKAN MINIMUM PADA SISTEM PENDULUM TERBALIK

This paper studies the optimal tracking error control problem on an inverted pendulum model. We characterize the optimal tracking error in term of pendulum’s parameters. Particularly, we derive the closed form expression for the pendulum length which gives minimum error. It is shown that the minimum error can always be accomplished as long as the ratio between the mass of the pendulum and that of the cart satisfies a certain constancy, regardless the type of material we use for the pendulum.

Alpha Uncertainty Principle

Alpha Uncertainty Principle introduces a new relationship between alpha potential and alpha uncertainty. Alpha uncertainty increases with degrees of freedom used in active management. This uncertainty cost has been largely ignored by investors. As a result free put options have been written to active managers, which if widespread could have systemic effects. The uncertainty principle introduces a trade-off that is shown to enable a new approach to a number of practical investment problems including: role of active management in asset allocation and optimal tracking error. The principle is shown to lead to the concept of Alpha Efficient Frontier.

Fund of Funds, Portable Alpha, and Portfolio Optimization

The authors examine the portfolio optimization problem that arises when a manager9s mandate is a fund of funds with an asset allocation benchmark. The portfolio manager9s objective is to maximize the portfolio excess return over the benchmark subject to given tracking errors. The authors decompose total tracking error into two components—the deviation from the benchmark and the additional risk factors associated with fund alpha. By quantifying the contribution of each component of portfolio excess return, the authors show that the performance of the style-constrained portfolio is determined by the active alpha–seeking skill of the portfolio manager and that fund alphas can be separated from their style loadings and are portable. These findings will not only help investors determine optimal tracking error constraints, but will also provide a framework for portfolio managers to identify funds with certain characteristics in order to achieve an optimal portfolio return. <b>TOPICS:</b>Manager selection, statistical methods, VAR and use of alternative risk measures of trading risk

Optimal tracking performance for SIMO systems

This note studies the optimal tracking problem for linear time-invariant single-input-multiple-output systems responding to a step reference signal. An integral square error criterion is used as the measure for tracking performance. Explicit expressions are developed for the optimal tracking error. These results characterize how nonsquare plants may pose additional difficulties for tracking, other than those resulted from nonminimum phase zeros and unstable poles.

Optimal tracking performance: preview control and exponential signals

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.