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Linear quadratic tracker (LQT) is usually employed to solve unconstrained tracking problems but falls short when dealing with systems exhibiting actuator saturation. This paper presents a novel quasilinear quadratic tracking method specifically designed to address this scenario. Firstly, the stochastic linearization (SL) approach is utilized to approximate the saturation nonlinearity with equivalent gains and biases using statistical properties of its input, which are thus incorporated into the system model so as to eliminate the nonlinearity. Then, different time scales are applied in the tracking controller and states in order to improve tracking accuracy. In addition, to reduce computational complexity, two algorithms are provided for approximating the equivalent gains and biases, catering to both scalar and vector control signals. Finally, the proposed algorithms are evaluated through numerical examples, demonstrating their effectiveness and superior tracking performances. [ABSTRACT FROM AUTHOR]

Although the data-driven control design techniques have gotten attention recently, few results address the tracking problem using data-based control formulations. Considering this, this paper presents a data-driven control method to drive the output of a system to its desired constant reference without using any model knowledge. To this end, first, this paper shows how to take the integral action into account for the data-driven control design for the reference tracking problem. Second, a closed-loop representation of the data-driven tracking controller with integral action is derived. Then, based on the representation, linear matrix inequality (LMI) conditions are derived for gain selection. The effectiveness of the proposed method is demonstrated using the speed control of a DC motor. Thanks to the integral action property, it is shown that the tracking error remains zero under constant disturbance affecting the system. [ABSTRACT FROM AUTHOR]

The classical quadratic regulator problem has rarely been studied for systems with persistent memory until recent times. In this paper, we studied the quadratic tracking problem on a finite time horizon for a system described by a controlled linear Volterra integrodifferential equation in $ \mathbb{R}^d $. We used the Fredholm equation approach and we obtained the synthesis of the optimal control in feedback form in terms of a Riccati differential equation, independent of the reference signal, and of two equations which instead depended on the known reference signal. To conclude the paper, we introduced a representation of the system in a history space. This space took into account the history of the system over a time interval of the same (finite) duration as that of the tracking problem under study. We related the equations used in the synthesis of the optimal control to a state space representation of the system with memory in the aforesaid history space. [ABSTRACT FROM AUTHOR]

Copyright of Ingenius, Revista Ciencia y Tecnología is the property of Universidad Politecnica Salesiana and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This article proposes a gain-scheduling procedure based on quasi-LPV modeling for a nonlinear coupled tank system to track the liquid level with zero steady-state error. The nonlinearities are directly represented by a parameter vector that varies within a bounded set constrained by the physical limits of the tank system levels. This approach enables accurate nonlinear system modeling using a linear parameter-varying model. State-feedback linear controllers are designed at the extreme vertices of the bounded set. The global controller is derived as the weighted average of local controller contributions, with the weighting determined by the instantaneous values of the parameter vector. Two interpolation mechanisms are proposed to implement this weighted averaging of the linear controllers. The results confirm the effectiveness of the proposed method in achieving accurate liquid level tracking.

This paper proposes a linear quadratic approximation approach to dynamic nonlinear rationally inattentive control problems with multiple states and multiple controls. An efficient toolbox to implement this approach is provided. Applying this toolbox to five economic examples demonstrates that rational inattention can help explain the comovement puzzle in the macroeconomics literature. [ABSTRACT FROM AUTHOR]

Abstract Facing to a planar tracking problem, a multiple-interpretable improved Proximal Policy Optimization (PPO) algorithm with few-shot technique is proposed, namely F-GBQ-PPO. Compared with the normal PPO, the main improvements of F-GBQ-PPO are to increase the interpretability, and reduce the consumption for real interaction samples. Considering to increase incomprehensibility of a tracking policy, three levels of interpretabilities has been studied, including the perceptual, logical and mathematical interpretabilities. Detailly speaking, it is realized through introducing a guided policy based on Apollonius circle, a hybrid exploration policy based on biological motions, and the update of external parameters based on quantum genetic algorithm. Besides, to deal with the potential lack of real interaction samples in real applications, a few-shot technique is contained in the algorithm, which mainly generate fake samples through a multi-dimension Gaussian process. By mixing fake samples with real ones in a certain proportion, the demand for real samples can be reduced.

Facing to a planar tracking problem, a multiple-interpretable improved Proximal Policy Optimization (PPO) algorithm with few-shot technique is proposed, namely F-GBQ-PPO. Compared with the normal PPO, the main improvements of F-GBQ-PPO are to increase the interpretability, and reduce the consumption for real interaction samples. Considering to increase incomprehensibility of a tracking policy, three levels of interpretabilities has been studied, including the perceptual, logical and mathematical interpretabilities. Detailly speaking, it is realized through introducing a guided policy based on Apollonius circle, a hybrid exploration policy based on biological motions, and the update of external parameters based on quantum genetic algorithm. Besides, to deal with the potential lack of real interaction samples in real applications, a few-shot technique is contained in the algorithm, which mainly generate fake samples through a multi-dimension Gaussian process. By mixing fake samples with real ones in a certain proportion, the demand for real samples can be reduced. [ABSTRACT FROM AUTHOR]

In this paper, for the output tracking problem of nonlinear discrete-time systems, a performance index is newly defined using the adaptive dynamic programming (ADP) technique to completely eliminate tracking errors in theory. In contrast to traditional definitions of performance indices in other ADP-based methods, the proposed performance index is not only designed from the perspective of output tracking errors but also introduced errors of system states and control inputs at adjacent stages, which is suitable for practical situations in many industrial applications, such as the alumina production, the flotation process, and the mineral grinding process. We proved that the obtained controller can make the system output fully track the given reference trajectory by applying the iterative criteria of the ADP technique. In addition, the proposed algorithm was implemented using a data-driven technique and neural networks to avoid analyzing and deducing the complicated dynamics of actual industrial processes. Finally, using historical data for a forced-circulation evaporation system in the alumina production process, the effect of the proposed approach was verified through a numerical simulation and compared with that of the proportional-integral controller. [ABSTRACT FROM AUTHOR]

Due to its extensive applications in different contexts, moving target tracking has become a hot topic in the last years, above all in the military field. Specifically, missile tracking research received a great effort, mainly for its importance in terms of security and safety. Herein, traditional solutions, e.g. Interacting Multiple Model (IMM) based on the Kalman estimation theory, achieve good performance under the main restrictive assumption of the a priori knowledge of the target model, so neglecting the unavoidable presence of model uncertainties and limiting the achievable tracking accuracy only by the presence of the measurement noise. With the specific aim of overcoming this narrowness, this work investigates the capability of deep neural networks in predicting the missile maneuvering trajectories in a model-free fashion. The idea is to leverage the Long-Short Term Memory (LSTM) net due to its excellent capability in learning long-term dependencies of temporal information. Two different LSTM-based architectures have been hence designed to predict both position and velocity of a missile using raw and noisy measurements provided by a realistic radar system, exploiting a large database abundant of realistic off-line data. Training results and theoretical derivations are verified through non-trivial scenarios in order to assess the capability of predicting unknown and realistic 3D missile maneuvers. Finally, the proposed approach has been also compared with a performing model-based IMM algorithm, suitably tuned to deal with realistic missile maneuvers, confirming the excellent generalization abilities of the developed data-driven architectures for different datasets.

For the first time, the problem of optimal tracking with a given reference trajectory and an integral quadratic performance criterion in the presence of singular perturbations is considered. The decomposition method is used to analyze singularly perturbed differential systems that arise in solving this problem. The method is based on the technique of integral manifolds of fast and slow motions. A suboptimal control is constructed the use of which leads to a difference in the values of the minimized functional for the optimal and suboptimal controls by an amount of the order of the second power of a small parameter characterizing singular perturbations. [ABSTRACT FROM AUTHOR]

We study optimal control problems in the multivariate linear‐quadratic‐Gaussian framework under rational inattention. We propose a three‐step procedure to solve this problem using semidefinite programming and derive the optimal signal structure without strong prior restrictions. We analyze both the transition dynamics of the optimal posterior covariance matrix and its steady state. We characterize the optimal information structure for some special cases and develop numerical algorithms for general cases. Applying our methods to solve three multivariate economic models, we obtain some results qualitatively different from the literature. [ABSTRACT FROM AUTHOR]

This paper presents a new design of model predictive control which combines non‐minimal state space (NMSS) and Laguerre functions. The utilization of NMSS omits the observer design process and brings convenience to multi‐input, multi‐output systems with time delay. But the dimensions of NMSS are high, which is harmful to online computation. The use of Laguerre functions helps reduce the data required in the optimization algorithm and makes up for the deficiency of NMSS. A modified solution for the optimal tracking problem using NMSS and Laguerre functions is proposed. Although the choice of the parameters in Laguerre functions needs experiments and experience, the method presented in this paper brings convenience to MPC design. Simulation results show that this approach not only reduces the computing effort without sacrificing the control performance significantly, but also has a good robustness to interference when tracking. [ABSTRACT FROM AUTHOR]

In the present article we investigate problems of tracking in the moving point control of thermal processes described by Fredholm integro-differential equations in partial derivatives with the Fredholm integral operator, in the case when the functions of point sources are nonlinear with respect to the control function. It is found that optimal controls are defined as solutions to a system of linear integral equations, and an algorithm for constructing its solution is developed. Sufficient conditions for the unique solvability of the tracking problem are found and an algorithm for constructing a complete solution to the nonlinear optimization problem was indicated.

We present an attracting cylinder method, which is a generalization of the invariant ellipsoid method to the cases of tracking and observation problems. Based on the method developed, we propose an algorithm for calculating the parameters of a controller ensuring the boundedness of the tracking or observation error in the presence of bounded exogenous disturbances. The efficiency of the approach proposed is demonstrated with examples. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Engineering Management / Gongcheng Guanli Xuebao is the property of Journal of Engineering Management Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this study, by means of the techniques of adaptive multi‐dimensional Taylor network (MTN) control, the tracking problem of a class of stochastic non‐linear systems with input delay is studied. Firstly, based on the Padé approximation method, a new variable is employed to overcome the problem of input delay, and MTNs are applied to estimate the non‐linear functions in the design of the controller. Secondly, an adaptive MTN controller design scheme is developed in the framework of backstepping. Thirdly, the stability of the closed‐loop system is analysed using Lyapunov's stability theory. Finally, the effectiveness of the proposed design approach is demonstrated by two examples. [ABSTRACT FROM AUTHOR]

A control problem for an operator differential equation in a Hilbert space is considered. The problem consists in constructing an algorithm generating a feedback control and guaranteeing that the solution of the equation follows a solution of another equation, which is subject to an unknown disturbance. We assume that both equations are given on an infinite time interval and the unknown disturbance is an element of the space of square integrable functions; i.e., the perturbation may be unbounded. We construct two algorithms based on elements of the theory of ill-posed problems and the extremal shift method known in the theory of positional differential games. The algorithms are stable with respect to information noises and calculation errors. The first and second algorithms can be used in the cases of continuous and discrete measurement of solutions, respectively. [ABSTRACT FROM AUTHOR]

In this paper, an approach to the construction of nonlinear output tracking control on a finite time interval for a class of weakly nonlinear systems with state-dependent coefficients is considered. The proposed method of control synthesis consists of two main stages. At the first stage, a nonlinear state feedback regulator is constructed by using a previously proposed control algorithm based on the State Dependent Riccati Equation (SDRE). At the second stage, the problem of fullorder observer construction is formulated and then it is reduced to the differential game problem. The form of its solution is obtained with the help of the guaranteed (minimax) control principle, which allows to find the best observer coefficients with respect to a given functional considering the worstcase uncertainty realization. The form of the obtained equations made it possible to use the algorithm from the first stage to determine the observer matrix. The proposed approach is characterized by the nonapplicability of the estimation and control separation principle used for linear systems, since the matrix of observer coefficients turned out to be dependent on the feedback coefficients matrix. The use of numerical-analytical procedures for determination of observer and feedback coefficients matrices significantly reduces the computational complexity of the control algorithm.

In this paper, we consider the problem of tracking a solution of a reference parabolic equation by a solution of another equation. A stable algorithm based on the extremal shift method is proposed for this problem. The algorithm is designed to work on a sufficiently large time interval where both equations operate.

This study deals with a tracking problem for hidden human targets using time-division multiple-input-multiple-output through-wall imaging radar (TWIR). An efficient image-domain tracking algorithm is proposed. Specifically, the authors first utilise back-projection algorithm and the phase coherence factor (PCF) to obtain multi-frame high quality images. Then a tracking algorithm via amplitude-distribution-based particle filter is proposed. Experimental data validates that this algorithm has a commendable effectiveness for hidden target tracking.

The paper considers the problem of a mobile two-wheeled robot control in the task of tracking a given position on the plane. The main idea is based on the use of multi-level decomposition during the synthesis of the control law. A distinctive feature of the considered problem statement is consideration of the actuators dynamic and the influence of external unknown disturbances. Using the synthesized control law, the asymptotic convergence of the robot to the path defined on the plane is ensured. [ABSTRACT FROM AUTHOR]

In this paper an approach for the construction of nonlinear output tracking control on a finite time interval for a class of weakly nonlinear systems with state-dependent coefficients is considered. The proposed method of control synthesis consists of two main stages. On the first stage, a nonlinear state feedback regulator is constructed using a previously proposed control algorithm based on the State-Dependent Riccati Equation (SDRE). On the second stage, the problem of full-order observer construction is formulated and then is reduced to the differential game problem. The form of its solution is obtained with the help of the guaranteed (minimax) control principle, which allows to find the best observer coefficients with respect to a given functional considering the worst-case uncertainty realization. The form of the obtained equations made it possible to use the algorithm from the first stage to determine the observer matrix. The proposed approach is characterized by the nonapplicability of the estimation and control separation principle used for linear systems, since the matrix of observer coefficients turned out to be dependent on the feedback coefficients matrix. The use of numerical-analytical procedures for determination of observer and feedback coefficients matrices significantly reduces the computational complexity of the control algorithm. [ABSTRACT FROM AUTHOR]

This study is concerned with a joint localisation and tracking problem for autonomous underwater vehicle (AUV), subject to asynchronous clock and stratification effect in cyber channels as well as the model disturbances in physical channels. The authors first construct an integrated state and clock model, which allows the co‐design of communication and control strategies. Then, an asynchronous localisation algorithm is developed to estimate the position of AUV, where the asynchronous clock and the stratification effect are both considered. With the estimated position information, a reinforcement learning based tracking controller is developed for the AUV to track the reference point. Particularly, the multivariate probabilistic collocation method is adopted to evaluate the model uncertainty. Moreover, the convergence analyses for the localisation algorithm and tracking controller are also given. Finally, simulation results are presented to show the effectiveness of the proposed method. It is demonstrated that the communication energy consumption and tracking error can be significantly reduced, through the co‐design of localisation and tracking strategies. [ABSTRACT FROM AUTHOR]

The robust linear tracking technique is applied to a practical path tracking problem for a ground vehicle modeled as a Dubins car. The tracking control is designed based on the optimal strategy in an auxiliary linear-quadratic differential game for a linearized vehicle model. In contrast with a purified theoretic setup, the real-life problem is complicated by a nonconstant speed and control saturation. Moreover, the actual path generating control can be unknown to the tracking strategy designer. These issues required additional design blocks: speed tracking loop and leading angle differentiation, both based on similar tracking algorithms. The saturation effect is considered by using command reinforcement. Numerical and experimental results are presented and compared. Robustness with respect to unknown disturbances is demonstrated. Novel analytic results on the tracking error/control effort tradeoff are also presented. [ABSTRACT FROM AUTHOR]

This study deals with a tracking problem for hidden human targets using time-division multiple-input-multiple-output through-wall imaging radar (TWIR). An efficient image-domain tracking algorithm is proposed. Specifically, the authors first utilise back-projection algorithm and the phase coherence factor (PCF) to obtain multi-frame high quality images. Then a tracking algorithm via amplitude-distribution-based particle filter is proposed. Experimental data validates that this algorithm has a commendable effectiveness for hidden target tracking. [ABSTRACT FROM AUTHOR]

The problem of the synthesis of a tracking system for electromechanical control objects is considered when measuring only the generalized coordinates of the mechanical subsystem. It is assumed that external and parametric perturbations act on the system. Assuming the smoothness of external perturbations and uncertainties, the mathematical model of the control object is presented in the form of a joint block form of controllability and observability relative to the coordinate basis of mixed variables (functions of state variables, external influences, and their derivatives). Based on these conditions of the joint block form of parametric uncertainty of the matrix before the control actions, a procedure for decomposition synthesis of the basic law of discontinuous control has been developed. The basic control law ensures exponential convergence of the generalized coordinates to the reference signals. To obtain estimates of the mixed variables used in the feedback, a method for synthesizing an observer of a lower order state with large coefficients is proposed, in which the principle of complete decomposition is implemented. The results of numerical modeling of the developed algorithms for a three-link manipulator operating in a cylindrical workspace under incomplete information conditions are presented. [ABSTRACT FROM AUTHOR]

We characterize the set of all trajectories T of an object t moving in a given corridor Y that are furthest away from a family S = { S } of fixed unfriendly observers. Each observer is equipped with a convex open scanning cone K(S) with vertex S. There are constraints on the multiplicity of covering the corridor Y by the cones K and on the "thickness" of the cones. In addition, pairs S, S′ for which [S, S′] ⊂ (K(S) ∩ K(S′)) are not allowed. The original problem max T min { d (t , S) : t ∈ T , S ∈ S } , where d(t, S) = ∥t − S∥ for t ∈ K(S) and d(t,S) = +∞ for t ∉ K(S), is reduced to the problem of finding an optimal route in a directed graph whose vertices are closed disjoint subsets (boxes) from Y \ ∪ S K (S) . Neighboring (adjacent) boxes are separated by some cone K(S). An edge is a part T (S) of a trajectory T that connects neighboring boxes and optimally intersects the cone K(S). The weight of an edge is the deviation of S from T (S) . A route is optimal if it maximizes the minimum weight. [ABSTRACT FROM AUTHOR]

We characterize the set of all trajectories T of an object t moving in a given corridor Y that are furthest away from a family S = { S } of fixed unfriendly observers. Each observer is equipped with a convex open scanning cone K(S) with vertex S. There are constraints on the multiplicity of covering the corridor Y by the cones K and on the "thickness" of the cones. In addition, pairs S, S′ for which [S, S′] ⊂ (K(S) ∩ K(S′)) are not allowed. The original problem max T min { d (t , S) : t ∈ T , S ∈ S } , where d(t, S) = ∥t − S∥ for t ∈ K(S) and d(t,S) = +∞ for t ∉ K(S), is reduced to the problem of finding an optimal route in a directed graph whose vertices are closed disjoint subsets (boxes) from Y \ ∪ S K (S) . Neighboring (adjacent) boxes are separated by some cone K(S). An edge is a part T (S) of a trajectory T that connects neighboring boxes and optimally intersects the cone K(S). The weight of an edge is the deviation of S from T (S) . A route is optimal if it maximizes the minimum weight. [ABSTRACT FROM AUTHOR]

Within the framework of the block approach, we propose a solution for a set of tasks for controlling a steam generator, i.e., a turbine unit under parametric uncertainty of the control object model, under the action of external uncontrolled disturbances and under incomplete measurements of the state vector. The feasibility of developed control algorithms has been confirmed by a simulation study in the Matlab-Simulink environment. [ABSTRACT FROM AUTHOR]

The concept of the hydraulic infinite linear actuator consists of two double-acting cylinders with hydraulically detachable pistons driving a common rod. Alternatingly, one cylinder engages and drives the load, whereas the other retracts; the actuator, thus, works in a kind of rope-climbing motion. The actuator has three degrees of freedom, which are temporarily coupled compared with one in a conventional cylinder. Hence, the actuator is a hybrid system with both continuous and discrete states and control inputs. This paper presents a tracking control problem and a solution for high-performance motion, which is interpreted as utilizing the hardware limits in the sense of velocity, accuracy, smoothness, and usability. The concept is demonstrated by simulation for the case of a rest-to-rest motion, but the intended use cases also include arbitrary trajectories. [ABSTRACT FROM AUTHOR]

In this study, the zero‐error convergence of the iterative learning control for a tracking problem is realised by incorporating a uniform quantiser with an encoding and decoding mechanism. Under this scheme, the system output is first transformed and encoded. Then, the encoded information is transmitted back for updating the input. The results are extended to a finite quantisation level situation under the same framework and a simulation using a permanent magnet linear motor is performed to demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

A method for solving the analysis problem of a linear control system with input and output disturbances is suggested. Its higher efficiency in comparison with the conventional approach is shown using an example of a test problem from COMPleib. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear distributed second order equation is considered. An algorithm for tracking a prescribed solution based on constructions of feedback control theory is designed. The algorithm is stable with respect to information noise and computation errors. It is designed for solutions in a sufficiently large time interval. [ABSTRACT FROM AUTHOR]