Optimal Finite-time Research Articles

Design of adaptive barrier function-based backstepping finite time guidance control for interceptor-target systems

This study introduces an optimal finite-time backstepping sliding mode guidance law, leveraging an adaptive continuous barrier function to examine the interceptor-target system’s motion in cylindrical coordinates. The integration of sliding mode and backstepping controllers enhances the robustness and performance of the proposed guidance method amidst external disturbances and model uncertainties. This combination also improves transient response, reduces chattering, and lowers control efforts. The adaptive continuous barrier function employed in this method eliminates the need for prior knowledge of the upper bounds of uncertainties and disturbances. Additionally, it ensures that adaptation gains are not overestimated, leading to more accurate performance and complete elimination of chattering. The Lyapunov stability theory is used to prove the finite-time convergence of the state trajectories of the interceptor-target system to a predefined neighborhood around the origin, despite external disturbances and uncertainties. A genetic optimization algorithm is utilized to optimally select the parameters of the guidance method. The efficacy of the proposed technique is validated through simulation results and real-time experiments on the Baseline Speedgoat Real-Time Target Machine platform. The method’s effectiveness and performance are further demonstrated through analysis and simulation in the MATLAB/Simulink environment.

Energetically Optimal Finite-Time Stabilization of Generalized Homogeneous Linear Systems

The problem of finite-time stabilization of a linear plant with an optimization of both a settling time and an averaged/weighted control energy is studied using the concept of generalized homogeneity. It is shown that the optimal finite-time stabilizing control in this case can be designed by means of solving a simple linear algebraic equation. Robustness of the obtained control law is studied.

Disturbance observer-based fuzzy adaptive optimal finite-time control for nonlinear systems

This paper investigates the issue of disturbance observer-based fuzzy adaptive optimal finite-time control in light of the backstepping approach for strict-feedback nonlinear systems with bias fault term and full state constraints. Considering that external disturbance and bias fault signal can affect the stability of control and control quality, a disturbance observer is constructed to track the external disturbances and bias fault online. A disturbance observer-based finite-time control strategy is proposed to achieve optimized control by utilizing the fuzzy logic system approximation-based adaptive dynamic programming method under the critic-actor framework. The purpose of the critic is to evaluate control performance and the role of the actor is to execute control behaviour. In addition, it is proved that the proposed fuzzy adaptive optimal finite-time scheme not only realizes all signals in closed-loop system are bounded, but also ensures that system states are restricted within specific sets. Finally, simulation results are shown to demonstrate the effectiveness of the proposed control strategy.

Distributed Finite-Time Safety Consensus Control of Vehicle Platoon With Senor and Actuator Failures

Due to the numerical subsystems and functionalities among the platoon, failures easily occur and lead vehicle safety and stability to deteriorate. With the surge of platoon connectivity, the abnormal states arising in faulty vehicles will have an impact on adjacent healthy vehicles, potentially resulting in severe traffic accidents. To address the aforementioned problems and improve the functional safety of platoons, a systemic anti-fault safety consensus strategy is proposed in this article to deal with sensor faults, LOE actuator faults, and bias actuator faults simultaneously. To tackle the necessary defects, this safety consensus technique can be split into fault detection tasks and fault-tolerant control tasks. Initially, a distributed finite-time observer is employed to detect sensor faults through the index between the reconstructed states and received states. In the presence of actuator faults, a novel adaptive finite-time fault parameter estimation law collaboration with a feasible differential observer is developed to assess the precise fault extent. In addition, to improve the estimation performance of the adaptive fault parameter estimation law, an integral discounted cost function is constructed in this paper to obtain the optimal learning gain. Via theoretical analysis, the solution for the minimal value of the cost function and the finite-time convergence property are demonstrated in this paper. Furthermore, by utilizing this novel adaptive optimal finite-time estimation law, a novel distributed adaptive finite-time fault-tolerant controller is constructed to compensate for failures in platoon. Finally, the effectiveness and feasibility of our safety consensus strategy are verified by real-time simulations through the dSPACE platform.

Minimally Dissipative Information Erasure in a Quantum Dot via Thermodynamic Length.

In this Letter, we explore the use of thermodynamic length to improve the performance of experimental protocols. In particular, we implement Landauer erasure on a driven electron level in a semiconductor quantum dot, and compare the standard protocol in which the energy is increased linearly in time with the one coming from geometric optimization. The latter is obtained by choosing a suitable metric structure, whose geodesics correspond to optimal finite-time thermodynamic protocols in the slow driving regime. We show experimentally that geodesic drivings minimize dissipation for slow protocols, with a bigger improvement as one approaches perfect erasure. Moreover, the geometric approach also leads to smaller dissipation even when the time of the protocol becomes comparable with the equilibration timescale of the system, i.e., away from the slow driving regime. Our results also illustrate, in a single-electron device, a fundamental principle of thermodynamic geometry: optimal finite-time thermodynamic protocols are those with constant dissipation rate along the process.

Adaptive Algorithm for Multi-Armed Bandit Problem with High-Dimensional Covariates

This article studies an important sequential decision making problem known as the multi-armed stochastic bandit problem with covariates. Under a linear bandit framework with high-dimensional covariates, we propose a general multi-stage arm allocation algorithm that integrates both arm elimination and randomized assignment strategies. By employing a class of high-dimensional regression methods for coefficient estimation, the proposed algorithm is shown to have near optimal finite-time regret performance under a new study scope that requires neither a margin condition nor a reward gap condition for competitive arms. Based on the synergistically verified benefit of the margin, our algorithm exhibits adaptive performance that automatically adapts to the margin and gap conditions, and attains optimal regret rates simultaneously for both study scopes, without or with the margin, up to a logarithmic factor. Besides the desirable regret performance, the proposed algorithm simultaneously generates useful coefficient estimation output for competitive arms and is shown to achieve both estimation consistency and variable selection consistency. Promising empirical performance is demonstrated through extensive simulation and two real data evaluation examples. Supplementary materials for this article are available online.

Deviation bounds and concentration inequalities for quantum noises

We provide a stochastic interpretation of non-commutative Dirichlet forms in the context of quantum filtering. For stochastic processes motivated by quantum optics experiments, we derive an optimal finite time deviation bound expressed in terms of the non-commutative Dirichlet form. Introducing and developing new non-commutative functional inequalities, we deduce concentration inequalities for these processes. Examples satisfying our bounds include tensor products of quantum Markov semigroups as well as Gibbs samplers above a threshold temperature.

Optimal finite-time Brownian Carnot engine.

Recent advances in experimental control of colloidal systems have spurred a revolution in the production of mesoscale thermodynamic devices. Functional "textbook" engines, such as the Stirling and Carnot cycles, have been produced in colloidal systems where they operate far from equilibrium. Simultaneously, significant theoretical advances have been made in the design and analysis of such devices. Here, we use methods from thermodynamic geometry to characterize the optimal finite-time nonequilibrium cyclic operation of the parametric harmonic oscillator in contact with a time-varying heat bath with particular focus on the Brownian Carnot cycle. We derive the optimally parametrized Carnot cycle, along with two other new cycles and compare their dissipated energy, efficiency, and steady-state power production against each other and a previously tested experimental protocol for the Carnot cycle. We demonstrate a 20% improvement in dissipated energy over previous experimentally tested protocols and a ∼50% improvement under other conditions for one of our engines, whereas our final engine is more efficient and powerful than the others we considered. Our results provide the means for experimentally realizing optimal mesoscale heat engines.

Artificial Intelligence of Things-Based Optimal Finite-Time Terminal Attractor and Its Application to Maximum Power Point Tracking of Photovoltaic Arrays in Smart Cities

The combination of artificial intelligence of things (AIoT) and photovoltaic power generation can save energy and reduce carbon emissions and further promote the development of smart cities. In order to obtain the maximum power output from photovoltaic (PV) arrays, we can use optimal maximum power point tracking (MPPT) technique with AIoT sensing to improve system efficiency. The optimal MPPT technique is the finite-time terminal attractor (FTTA) based on the gradient particle swarm optimization (GPSO), which can be applied to track the maximum power of a PV array system. The FTTA not only provides fast finite-time convergence but also attenuates steady-state errors, making it ideal for nonlinear system applications. The GPSO is used to search the control parameters of the FTTA, which is able to find the global best solution. This avoids unmodeled dynamic behavior of the system excited by the quiver, which slows down the control convergence and prematurely traps the system into a local optimum. The MATLAB computer software is used to simulate the proposed PV maximum power point tracking system. The results show that more accurate and better tracking control of the PV array can be produced under partial shading conditions and then improve the steady-state and transient performance.

Optimality of nonconservative driving for finite-time processes with discrete states.

An optimal finite-time process drives a given initial distribution to a given final one in a given time at the lowest cost as quantified by total entropy production. We prove that for a system with discrete states this optimal process involves nonconservative driving, i.e., a genuine driving affinity, in contrast to the case of a system with continuous states. In a multicyclic network, the optimal driving affinity is bounded by the number of states within each cycle. If the driving affects forward and backwards rates nonsymmetrically, the bound additionally depends on a structural parameter characterizing this asymmetry.

Theoretical and experimental investigations on modified LQ terminal control scheme of piezo-actuated compliant structures in finite time

This study focuses on the open-loop dynamic shape control to realize a rapid and smooth morphing process for a flexible plate which is actuated by a macro fiber composite patch. A finite element model of the system is established and verified for theoretical investigations. Steady-state and dynamic analyses are carried out to satisfy the desired rest-to-test morphing requirement. Spurious oscillations and large overshoots are observed while applying some common voltage signals. The results imply that the voltage profile of the actuator plays a key role in the dynamic morphing behavior of the system. Therefore, a quantitative criterion is proposed to determine the critical voltage slope for evaluating the boundary between quasi-static and dynamic processes. An optimal finite-time feedforward control approach named “modified linear quadratic (LQ) terminal controller” is proposed to optimize the voltage profiles by simultaneously considering the suppression of transient and residual vibration. The superiority of the proposed open-loop control scheme is appreciated when it is compared with the standard LQ terminal controller. An experimental setup is designed for verification. The effectiveness of the theoretical model is validated through modal analysis, static deformation, and dynamic responses. It is indicated by the experiment results that rapid and smooth dynamic shape morphing processes with negligible vibration within a short period of time can be achieved using the optimized voltage profile.

The Quantum Friction and Optimal Finite-Time Performance of the Quantum Otto Cycle.

In this work we considered the quantum Otto cycle within an optimization framework. The goal was maximizing the power for a heat engine or maximizing the cooling power for a refrigerator. In the field of finite-time quantum thermodynamics it is common to consider frictionless trajectories since these have been shown to maximize the work extraction during the adiabatic processes. Furthermore, for frictionless cycles, the energy of the system decouples from the other degrees of freedom, thereby simplifying the mathematical treatment. Instead, we considered general limit cycles and we used analytical techniques to compute the derivative of the work production over the whole cycle with respect to the time allocated for each of the adiabatic processes. By doing so, we were able to directly show that the frictionless cycle maximizes the work production, implying that the optimal power production must necessarily allow for some friction generation so that the duration of the cycle is reduced.

SDRE based optimal finite-time tracking control of a multi-motor driving system

This paper presents a nonlinear optimal finite-time tracking controller based on a state-dependent Riccati equation (SDRE) for the multi-motor driving system (MDS). Conventional fast terminal sliding mode controller (FTSMC) can get the finite-time convergence of the tracking error, but how to achieve the optimality simultaneously is not an easy task. To address this optimal control problem, a SDRE based optimal controller is developed via a fast terminal sliding surface to design the nonlinear optimal feedback of the FTSMC. To further increase the robustness of the SDRE based method, an extended state observer (ESO) and a robust controller are incorporated into the optimal controller design to deal with the system uncertainties and external disturbances. Consequently, the proposed controller can not only guarantee the finite-time stability of the tracking error, but also achieve the optimal control performance under the system unknown dynamics. Experimental results demonstrate the effectiveness of the proposed scheme.

Application of Single- and Multi-Objective Evolutionary Algorithms for Optimal Nonlinear Controller Design in Boiler–Turbine System

This paper presents an application of evolutionary algorithm techniques for optimal nonlinear controller design in drum-type boiler–turbine system. Designing of controller for third-order boiler–turbine system is always a complicated task due to the presence of highly interactive nonlinearities. The present work is the first one which attempts to design and implement recently developed finite time convergent controller in third-order boiler–turbine dynamics, and it is described as multi-input–multi-output (MIMO) nonlinear system. The present work explores the possibility of application of single-objective and multi-objective evolutionary algorithm techniques toward optimal tuning of finite time convergent controller to achieve the desired performance for third-order boiler–turbine system. The single-objective evolutionary algorithm techniques such as real-coded genetic algorithm (RGA), modified particle swarm optimization (MPSO), differential evolution (DE), and self-adaptive differential evolution (SADE) are implemented with the minimization of integral square error (ISE) as an objective to obtain optimal tuning parameters. Also, the present paper explores the possibility of simultaneous minimization of conflicting objectives such as ISE and computational cost of the proposed controller using multi-objective evolutionary algorithms such as non-dominated sorting genetic algorithm (NSGA) and modified non-dominated sorting genetic algorithm-II (MNSGA-II). The performance of the proposed optimal finite time convergent controller is validated by simulating different kinds of set point changes, and the obtained results are presented as various case studies. The adaptability of the proposed controller during parameter variations is also examined. The performance of the single-objective and multi-objective evolutionary algorithms has been statistically analyzed, and the results are reported. The results reveal that among the four single-objective EA techniques, SADE offers better performance due to its inherit self-adaptive capability. Also, during multi-objective optimization, MNSGA-II has provided better solution due the presence of dynamic crowding distance (DCD) and control elitism (CE) strategies.

Stochastic finite-time partial stability, partial-state stabilization, and finite-time optimal feedback control

In many practical applications, stability with respect to part of the system’s states is often necessary with finite-time convergence to the equilibrium state of interest. Finite-time partial stability involves dynamical systems whose part of the trajectory converges to an equilibrium state in finite time. In this paper, we address finite-time partial stability in probability and uniform finite-time partial stability in probability for nonlinear stochastic dynamical systems. Specifically, we provide Lyapunov conditions involving a Lyapunov function that is positive definite and decrescent with respect to part of the system state and satisfies a differential inequality involving fractional powers for guaranteeing finite-time partial stability in probability. In addition, we show that finite-time partial stability in probability leads to uniqueness of solutions in forward time and we establish necessary and sufficient conditions for almost sure continuity of the settling-time operator of the nonlinear stochastic dynamical system. Finally, we develop a unified framework to address the problem of optimal nonlinear analysis and feedback control design for finite-time partial stochastic stability and finite-time, partial-state stochastic stabilization. Finite-time partial stability in probability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function that is positive definite and decrescent with respect to part of the system state and can clearly be seen to be the solution to the steady-state form of the stochastic Hamilton–Jacobi–Bellman equation guaranteeing both finite-time, partial-state stability and optimality. The overall framework provides the foundation for extending stochastic optimal linear–quadratic controller synthesis to nonlinear–nonquadratic optimal finite-time, partial-state stochastic stabilization.

Finite-time partial stability and stabilization, and optimal feedback control

In this paper, we develop a unified framework to address the problem of optimal nonlinear analysis and feedback control design for finite-time partial stability and finite-time, partial-state stabilization. Finite-time partial stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function that is positive definite and decrescent with respect to part of the system state, satisfies a differential inequality involving fractional powers, and can clearly be seen to be the solution to the steady-state form of the Hamilton-Jacobi-Bellman equation guaranteeing both partial stability and optimality. The overall framework provides the foundation for extending optimal linear-quadratic controller synthesis to nonlinear-nonquadratic optimal finite-time, partial-state stabilization. In addition, we specialize our results to address the problem of optimal finite-time control for nonlinear time-varying systems. Finally, we develop optimal feedback controllers for affine nonlinear systems using an inverse optimality framework tailored to the finite-time, partial-state stabilization problem and use this result to address finite-time, partial-state stabilizing sublinear controllers that minimize a derived performance criterion involving subquadratic terms.

Synchronization of Lorenz System Based on Fast Stabilization Sliding Mode Control

A sliding mode control approach is achieved for Lorenz system based on optimal finite time convergent and integral sliding mode surface. The system perturbation is divided into two parts: the unmatched and the matched parts. Firstly, we design a discontinuous control for the unmatched part which will not be amplified. Secondly, we design a continuous control, that is, the ideal control to stabilize the Lorenz system error states in finite time stabilization. Then the controller based on integral sliding mode is constructed to ensure the robustness. The proposed method is proven to guarantee the stability and the robustness using the Lyapunov theory in the system uncertainties and external perturbation. Finally, the numerical simulations demonstrate that the proposed controller is effective and robust with respect to the perturbation.

A new switching design to finite-time stabilization of nonlinear systems with applications to neural networks

This paper is concerned with the optimal finite-time stabilization problem for nonlinear systems. For the given stabilization strength, a new switching protocol is designed to stabilize the system with a fast speed. The obtained protocol covers both continuous control and discontinuous one under the framework of Filippov solutions. Some criteria are discussed in detail on how to choose an optimal protocol such that the finite stabilization time can be shortened. Finally, the main theory results are applied to the general neural networks by one numerical example to illustrate the effectiveness of the proposed design method.

Optimal Finite-Time State Estimation for Discrete-Time Switched Systems under Switching Frequency Constraint

The state estimation problem for a class of switched linear systems which only switches in some short interval is addressed. Besides the asymptotic stability of error dynamics, the boundness of error state is a significant issue for short-time switched systems. By introducing the concept of finite-time stability, the state estimation procedure is formulated to determine appropriate observer gains ensuring the error dynamics is finite-time stable in the short-time switching intervals of interest. Optimal finite-time observers are designed through iterative algorithms to minimize the bound of error state, in the cases with and without disturbances. Particularly, when the total activation time is known, a less conservative result can be derived and an optimization problem can be solved with the help of the genetic algorithm. A numerical example is provided to illustrate the theoretical findings in this paper.

Optimal finite-time passive controller design for uncertain nonlinear Markovian jumping systems

This paper studies the optimal finite-time passive control problem for a class of uncertain nonlinear Markovian jumping systems (MJSs). The Takagi and Sugeno (T–S) fuzzy model is employed to represent the nonlinear system with Markovian jump parameters and norm-bounded uncertainties. By selecting an appropriate Lyapunov-Krasovskii functional, it gives a sufficient condition for the existence of finite-time passive controller such that the uncertain nonlinear MJSs is stochastically finite-time bounded for all admissible uncertainties and satisfies the given passive control index in a finite time-interval. The sufficient condition on the existence of optimal finite-time fuzzy passive controller is formulated in the form of linear matrix inequalities and the designed algorithm is described as an optimization one. A numerical example is given at last to illustrate the effectiveness of the proposed design approach.