Finite-horizon Tracking Control Research Articles

Data-Driven Finite-Horizon Tracking Control With Event-Triggered Mechanism for the Continuous-Time Nonlinear Systems.

In this article, the neural network (NN)-based adaptive dynamic programming (ADP) event-triggered control method is presented to obtain the near-optimal control policy for the model-free finite-horizon optimal tracking control problem with constrained control input. First, using available input-output data, a data-driven model is established by a recurrent NN (RNN) to reconstruct the unknown system. Then, an augmented system with event-triggered mechanism is obtained by a tracking error system and a command generator. We present a novel event-triggering condition without Zeno behavior. On this basis, the relationship between event-triggered Hamilton-Jacobi-Isaacs (HJI) equation and time-triggered HJI equation is given in Theorem 3. Since the solution of the HJI equation is time-dependent for the augmented system, the time-dependent activation functions of NNs are considered. Moreover, an extra error is incorporated to satisfy the terminal constraints of cost function. This adaptive control pattern finds, in real time, approximations of the optimal value while also ensuring the uniform ultimate boundedness of the closed-loop system. Finally, the effectiveness of the proposed near-optimal control pattern is verified by two simulation examples.

Finite-horizon tracking control for a class of stochastic systems subject to input constraints and hybrid cyber attacks

This paper is concerned with the probabilistic-constrained finite-horizon tracking control problem for a class of stochastic systems subject to randomly occurring hybrid cyber attacks and input constraints. Both the randomly occurring denial-of-service (DOS) attacks and randomly occurring deception attacks are considered in an unified framework. The purpose of the current study is to design an observer-based tracking controller such that: over a finite horizon, (1) the variance of the estimation error is less than certain bound at each time step, (2) the probability of the tracking error falling in certain region should larger than a specified value and the region is minimized at each time step. To achieve those purposes, an improved multi-dimensional Chebyshev inequality method is first utilized to convert the probabilistic constraint to a deterministic one. Then an observer-based tracking control method is designed to estimate the state and design the tracking controller, which are realized through solving a set of recursive linear matrix inequalities. By using the proposed algorithm, the observer and tracking controller gains can be solved out in terms of the solution to a convex optimization problem. A simulation example is finally given to demonstrate the effectiveness and applicability of the proposed method.

Simulation of Observer Based Tracking Control for the Longitudinal Dynamics Model of a Vertical Takeoff and Landing Aircraft

The article describes a method for constructing a nonlinear finite-horizon tracking control for the output of a weakly nonlinear dynamic system obtained by the author earlier and also presents the results of numerical experiments, which have used this method to control the output of the longitudinal dynamics model of a vertical takeoff and landing aircraft. The article aim is to demonstrate a performance capability of the method for non-weakly non-linear systems, as well as to evaluate the effectiveness of the obtained control in comparison with linear analogues.The method is based on the approximate solution of a matrix Riccati-like differential equation with state dependent coefficients. In the English literature, such a constructing approach to control is called a SDRE technique. The latter has become quite widespread in practical applications due to the relative ease of implementation. The disadvantage of the SDRE technique is that there is the need to numerically solve the Riccati-like matrix equation in the course of operation for each new system state, which may come up against the limited computational resources. To overcome this drawback, a number of methods for approximate solution of this equation were developed, including that of for the finite-horizon tracking problem.A feature of the method under study is an approach to the approximate equation solution based on the formal asymptotic small- parameter expansion of this solution in case of system nonlinearity. A numerical-analytical procedure for constructing the control was obtained. In contrast to the known results, with such an approach there is no need to perform a number of computationally expensive operations in the control process. This allows potential application of this method for problems with highly limited computational resources, for example for the problem of an autonomous robotic control.The article considers several scenarios where initial conditions of the aircraft dynamics model differ from each other. It is shown that in most cases, the obtained nonlinear controls exceed the linear analogues by the quadratic quality criterion considered.

Finite-Horizon Tracking Control for Repetitive Systems with Uncertain Initial Conditions

Finite-Horizon Tracking Control for Repetitive Systems with Uncertain Initial Conditions