Robust Optimal Control Design Research Articles

Robust-optimal control design for current-controlled electromagnetic levitation system with unmatched input uncertainty

Robust-optimal control design for current-controlled electromagnetic levitation system with unmatched input uncertainty

A robust optimal distributed control design for simultaneous voltage regulation and current sharing in DC microgrid

AbstractIn this article, a robust optimal distributed controller is designed for achieving average voltage regulation and current sharing in a DC microgrid. Each distributed generation unit (DGU) consists of a DC‐DC buck converter that supplies a local constant current load. The proposed controller only utilises output currents of converters and the possible maximum error values in estimation of series resistance in the RLC filter used in each DGU. The proposed controller is formed such that the possible estimation error is considered as an uncertain parameter. In addition to obtaining two main objectives, average voltage regulation, and current sharing, a robust control problem is solved through an optimal control technique to calculate controller parameters such that the stability of the grid is guaranteed. The stability of the closed loop system with parametric uncertainty is proved through Lyapunov analysis. The closed loop system with the suggested controller is tested by simulations and through different scenarios to reveal the reliable and satisfactory performance of the proposed robust optimal control structure.

Learning-based robust optimal tracking controller design for unmanned underwater vehicles with full-state and input constraints

In this article, the optimal tracking control problem for unmanned underwater vehicles (UUVs) with full-state and input constraints under the presence of external disturbances and internal dynamic uncertainties is addressed. To achieve preassigned state constraints on UUVs, the traditional UUVs model is transformed into an unconstrained one by using two different nonlinear mappings (NMs). Then the robust tracking control problem of traditional UUVs model under position/Euler angles and velocity constraints is transformed to an optimal control problem of the transformed system without any constraints. A learning-based optimal control method is designed to solve the optimal control problem of the transformed system by employing the optimized backstepping (OB) paradigm and reinforcement-learning (RL) technique, achieving uniformly ultimately boundedness (UUB) subject to optimal cost. To deal with lumped disturbances for the velocity control loop, a neural-network (NN) identifier is employed and incorporated into actor–critic architecture, attaining robust tracking performance. Due to the adopted nonquadratic cost function with respect to the control input, the optimal control solution is established in the form of a hyperbolic tangent function to handle the input constraints. Compared with traditional PID method and MPC approach, the proposed controller can improve tracking performance of UUV by 32.04% and 79.64%, respectively.

Robust Inverse Optimal Cooperative Control for Uncertain Linear Multiagent Systems

This article studies robust inverse optimal control design for cooperative control of uncertain linear multiagent systems (MASs) on directed graph. While designing optimal cooperative control solutions are desired and have been widely considered, ignoring the system uncertainties during the design phase can jeopardize their performance and even cause instability during the operation phase. To alleviate this issue, distributed controllers are designed that are robust to uncertainty and are optimal with respect to some meaningful performance index (referred to as being inverse optimal). It is shown that using the presented distributed robust inverse optimal controller the network of agents converge to a common value of interest or follow the trajectory of a leader node despite uncertainties. A comprehensive study is performed with the time varying bounded parameters uncertainties on the drift and the input matrices of the state-space representation of the MASs. Sufficient conditions for stability analysis are provided using the Lyapunov theory to show that the distributed controller can stabilize the MAS globally. The proposed ideas are confirmed via numerical examples.

Robust Optimal Control Design for Performance Enhancement of PWM Voltage Source Inverter.

PWM (pulse-width modulation) voltage source inverters are used in a wide range of AC power systems where the output voltage must be controlled to follow a sinusoidal reference waveform. In order to achieve precision and fast-tracking control, restrictive sliding mode control (RSMC) provides a fast system state convergence time. However, the RSMC still suffers from the chattering problem, which leads to high harmonic distortion and slow response of the inverter output state. Furthermore, the load of the inverter may be severe load changing and the control parameters become difficult to adjust, worsening the adaptability to achieve the desired control of the inverter output. In this paper, a robust optimal control design comprised of an enhanced restrictive sliding mode control (ERSMC) and density particle swarm optimization (DPSO) algorithm is proposed, and then applied to PWM voltage source inverters. The ERSMC not only has finite time convergence but also provides chatter elimination. The DPSO is highly adaptable for acquiring the control parameters of the ERSMC and finding the best solution in the global domain. The proposed controller is realized for the actual PWM voltage source inverter controlled by a TI DSP-based development platform, so that the inverter output voltage has fast dynamic response and satisfactory steady-state behavior despite high load changing and non-linear disturbances.

Optimized Bézier-curve-based command generation and robust inverse optimal control for attitude tracking of spacecraft

In this paper we address the optimized attitude command generation and robust inverse optimal control design for the spacecraft attitude tracking with large angle slews. Firstly, with the reference attitude command described in a Bézier curve through the spherical linear interpolation, an optimized reference command is generated to meet the principles of small energy consumption and short turning time. The applied optimization combines the particle swarm optimization algorithm and genetic algorithm based on information entropy to guarantee the diversity of the population and improve the global search capabilities. Next, a robust inverse optimal control is developed for the attitude tracking of the obtained optimized reference attitude command, consisting of an inverse optimal Lyapunov approach for performance guarantee and an arctangent-based integral sliding mode control for the disturbance attenuation. A stronger generality of the control Lyapunov function is obtained for the inverse optimality. Furthermore, the developed control efforts are of smaller amplitudes due to introducing the auxiliary angular velocity for the smooth transition to the reference attitude command. Finally, simulation results are included to show the performance of the proposed scheme.

Fuzzy-set theory based optimal robust constraint-following control for permanent magnet synchronous motor with uncertainties

This paper proposes a novel optimal robust control design approach to address the high-performance trajectory tracking control problem for the permanent magnet synchronous motor (PMSM) system containing uncertainties by integrating the Udwadia–Kalaba theory and the fuzzy set theory. First, the uncertainties in the PMSM system are described as fuzzy uncertainties based on fuzzy set theory. Second, a deterministic robust control scheme is proposed based on the servo constraint control approach and the fuzzy estimated bound of uncertainties. The proposed control scheme’s objective is to guarantee the uncertain PMSM system to achieve deterministic performance: uniformly bounded and uniformly ultimately bounded. Third, based on the fuzzy description of uncertainties, a fuzzy performance index including steady-state controlled performance and control cost is constructed. An optimal parameters design problem of the proposed control is presented and solved by minimizing the fuzzy performance index with a unique analytic-form solution. The resulting control renders the uncertain PMSM system strictly to follow the servo constraint, and the fuzzy performance is optimized. Ultimately, simulations and experiments illustrate that the proposed control approach has excellent constraint tracking performance for PMSM systems with uncertainties.

Nash game‐based adaptive robust control design optimization for the underactuated mechanical system with fuzzy evidence theory

AbstractThis article proposes a novel Nash game‐theoretical optimal adaptive robust control design approach to address the constraint‐following control problem for the uncertain underactuated mechanical systems with fuzzy evidence theory. First, the uncertainty is considered bounded and the bound is unknown but lies in a specified fuzzy evidence number. Second, a deterministic adaptive robust control scheme is proposed based on the servo constraint following control method, which renders the uncertain underactuated mechanical system to follow the specified constraints accurately with deterministic performance (guarantee uniform boundedness and uniform ultimate boundedness). It is shown that the designed self‐adjusting leakage‐type adaptive law can compensate for the uncertainty and avoid overcompensation. Third, based on the performance analysis and the fuzzy evidence description of uncertainty, the Nash game theory is introduced into the multi‐parameter optimization design for the two tunable control gains selected as two players. The cost functions for two players are relevant to the system constraint‐following performance and control cost. Then we can obtain the optimal control gains by seeking the Nash equilibrium which is always proved to exist. Ultimately, the simulation results on the two‐wheeled self‐balancing robot demonstrate the availability of the proposed control scheme and the optimal design approach for the underactuated mechanical systems with uncertainties.

Designing Robust Control for Permanent Magnet Synchronous Motor: Fuzzy Based and Multivariable Optimization Approach

This article proposed a novel optimal robust control design approach to solve the uncertain parameter problem in the permanent magnet synchronous motor (PMSM) system by integrating the fuzzy set theory and system control theory. First, we adopt the prescribed fuzzy number to describe the time-varying but bounded uncertain parameter in the PMSM system. Second, based on the estimated bound of the uncertain parameter and the nominal dynamical model, we design a deterministic robust control scheme characterized by model-based control and feedback control. The control objective is to guarantee the PMSM system with uncertain parameters satisfies the desired motion equation with deterministic system performance: uniform boundedness (UB) and uniform ultimate boundedness (UUB). Third, using the fuzzy uncertain parameter, a performance index relevant to the steady-state performance and control cost is constructed. A parameters design optimization problem is formulated by minimizing the performance index, whose analytical solution is successfully solved and proved to always exists and is unique. As a result, the resulting PMSM system under the proposed control approach has two-level system performance: the guaranteed deterministic performance and optimal performance. Finally, the results of numerical simulation and experiment are presented for demonstration.

Robust ℓ₁-Controller Design for Discrete-Time Positive T–S Fuzzy Systems Using Dual Approach

In this article, a new approach is proposed for stability analysis and controller design of nonlinear discrete-time positive systems by means of the Takagi&#x2013;Sugeno fuzzy model. The closed-loop stability and the positivity constraint are guaranteed by synthesizing a linear co-positive Lyapunov function and by applying the parallel distributed compensation controller. In contrast to the state-of-the-art approaches for ensuring the <inline-formula> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula>-stability of the positive system which are based on bilinear matrix inequalities, the proposed optimal robust control design under <inline-formula> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula>-induced performance is derived based on linear programming framework. It has been shown that the computational complexity of the proposed optimization problem can be effectively reduced. Finally, a numerical example and the Leslie population model are adopted to show the capabilities of the proposed method.

Optimal robust model predictive reset control design for performance improvement of uncertain linear system

This study aims to design a robust reset dynamic output feedback control (DOFC) for a class of uncertain linear systems. This procedure is performed as following. First, the elements of the robust DOFC are designed via the linear matrix inequality (LMI) technique such that closed-loop exponential stability is achieved. Second, reset law which contains value of after reset and a constraint for the reset action is determined. Genetic algorithm (GA) is applied to minimize the proposed objective function to find the reset times by using the specified after reset value for individual reset instances. To do this, a model-predictive-based optimization is adopted by using output information. The proposed robust controller is applied to two uncertain systems; distillation column, and B747-100/200 aircraft model. The merits of the proposed robust reset controller in improving transient performance are demonstrated by comparing its results with state-of-the-art methods.

Robust optimal feedback control design for uncertain systems based on artificial neural network approximation of the Bellman’s value function

In this study, a local approximated solution for the Hamilton–Jacobi–Bellman equation based on differential neural networks is proposed. The approximated Value function is used to obtain a feedback control law for a class of uncertain dynamical systems. The approach to deal with the uncertainties of the dynamical system is a min–max method that yields obtaining a robust-like solution for an optimal control problem. The proposed cost functional is presented in the Bolza form and the necessary and sufficient conditions for getting the min–max optimal solution with the designed robust version of the dynamic programming approach are provided. Moreover, the effect of the neural network approximation is studied. All the analysis considers a smoothness assumption regarding the Value function. The practical stability of the system with the neural network feedback optimal control is formally demonstrated by means of the Lyapunov method. Finally, the performance of the control law is compared in simulation with a classical optimal controller. The proposed controller overcomes the results produced by the classical controller, which is confirmed by the functional evaluation.

A New Design Scheme for Intelligent Upper Limb Rehabilitation Training Robot.

In view of the urgent need for intelligent rehabilitation equipment for some disabled people, an intelligent, upper limb rehabilitation training robot is designed by applying the theories of artificial intelligence, information, control, human-machine engineering, and more. A new robot structure is proposed that combines the use of a flexible rope with an exoskeleton. By introducing environmentally intelligent ergonomics, combined with virtual reality, multi-channel information fusion interaction technology and big-data analysis, a collaborative, efficient, and intelligent remote rehabilitation system based on a human’s natural response and other related big-data information is constructed. For the multi-degree of the freedom robot system, optimal adaptive robust control design is introduced based on Udwdia-Kalaba theory and fuzzy set theory. The new equipment will help doctors and medical institutions to optimize both rehabilitation programs and their management, so that patients are more comfortable, safer, and more active in their rehabilitation training in order to obtain better rehabilitation results.

Output feedback control of electrolyte flow rate for Vanadium Redox Flow Batteries

In this paper, we propose a new strategy for electrolyte flow rate control in Vanadium Redox Flow Batteries. The keystone of our approach is a novel methodology for determination of optimal reference voltage and robust feedback controller design that provides the desired transient and steady state battery performance. In addition, we introduce a hierarchical scheme of the general battery control system that significantly simplifies classification of battery control tasks and gives guidelines for multistage controller design. The research considers a kilo-watt class VRFB system operating in a wide range of loading currents (20–180 A). The proposed control algorithm allows reference trajectory tracking with high accuracy (average error less than 0.0005%), yet providing the required battery performance at twice lower flow rates as compared to the existing solutions, and thus, decreasing pump energy consumption by a factor of 3. As a result, the proposed method can be used for flow rate regulation in practical VRFB systems ensuring their stable and efficient operation under dynamic loading conditions.

A New Multi-objective Artificial Bee Colony Algorithm for Optimal Adaptive Robust Controller Design

Artificial bee colony algorithm as a recent meta-heuristic algorithm, inspired from the foraging behavior of honey bees, can be considered as a proper technique to handle optimization problems. In this paper, a multi-objective artificial bee colony algorithm is introduced in which an archive is defined to store non-dominated solutions. Furthermore, to reduce computations and to have evenly distributed solutions, the archive is pruned using a technique based on neighborhood radius concepts. A group of bees that is responsible for improvement of the solutions chooses and exploits one solution of the archive. Because of the definition of neighborhood radius and retaining adjacent solutions, the remaining solutions have an equal chance to be selected by onlooker bees. In order to examine the proposed algorithm, some benchmark functions are used and the results are compared with true Pareto fronts. Moreover, the algorithm is utilized to optimize the coefficients of a new combined controller applied to a ball-beam system. In fact, the proposed controller is a combination of robust decoupled sliding mode and adaption laws based on the gradient decent method. The objective functions are considered as the integral time of absolute of errors of the ball position and the beam angle that should be minimized with a constraint on the control effort. To evaluate and validate the suggested approach, the obtained time responses of the ball-beam system are compared with those of other recently reported controllers.

Control allocation-based fault tolerant control

This paper describes a novel scheme for fault tolerant control using a robust optimal control design method. This scheme can also be employed as actuator redundancy management for over-actuated linear systems. In contrast to many existing methods in the literature, this scheme can be applied to systems whose control input matrix cannot be factorised into two matrices whose ranks are equal and less than the minimum of the number of columns and rows of the input matrix. The so-called virtual control, in this scheme, is calculated using a robust ℋ2-based feedback design approach constructed to be robust against uncertainties emanating from visibility of the control allocator to the controller and imperfection in the estimated effectiveness gain. Then, using a new control allocation scheme along with a novel Tikhonov-based re-distributor mechanism, the obtained virtual control signal is re-distributed among remaining (redundant or non-faulty) set of actuators. As the proposed scheme is modular-based, it can be employed as a real-time fault tolerant control scheme with no need to reconfigure the controller in the case of actuator faults or failures. The effectiveness of the proposed scheme is demonstrated by a numerical example.

Robust optimal PID controller design for attitude stabilization of flexible spacecraft

Robust optimal PID controller design for attitude stabilization of flexible spacecraft

A Fuzzy Approach for Optimal Robust Control Design of an Automotive Electronic Throttle System

In this paper, we propose a fuzzy approach for optimal robust control design of an automotive electronic throttle (ET) system. Compared with the conventional ET control systems, we establish the fuzzy dynamical model of the ET system with parameter uncertainties, nonlinearities, and external disturbances, which may be nonlinear, (possibly fast) time varying. These uncertainties are assumed to be bounded, and the knowledge of the bound only lies within a prescribed fuzzy set. A robust control that is deterministic and is not the usual if–then rules-based control is presented to guarantee the controlled system to achieve the deterministic performance: uniform boundedness and uniform ultimate boundedness. Furthermore, a fuzzy-based system performance index including average fuzzy system performance and control cost is proposed based on the fuzzy information. The optimal design problem associated with the control can then be solved by minimizing the fuzzy-based performance index. With this optimal robust control, the performance of the fuzzy ET system is both deterministically guaranteed and fuzzily optimized.

Robust Optimal Controller Design for Generic Hypersonic Vehicles

AbstractIn this paper, a robust optimal controller design problem is investigated for the longitudinal dynamics of generic hypersonic vehicles. The vehicle dynamics involve parametric uncertainties...

Robust optimal control with adjustable uncertainty sets

In this paper, we develop a unified framework for studying constrained robust optimal control problems with adjustable uncertainty sets. In contrast to standard constrained robust optimal control problems with known uncertainty sets, we treat the uncertainty sets in our problems as additional decision variables. In particular, given a finite prediction horizon and a metric for adjusting the uncertainty sets, we address the question of determining the optimal size and shape of the uncertainty sets, while simultaneously ensuring the existence of a control policy that will keep the system within its constraints for all possible disturbance realizations inside the adjusted uncertainty set. Since our problem subsumes the classical constrained robust optimal control design problem, it is computationally intractable in general. Nevertheless, we demonstrate that by restricting the families of admissible uncertainty sets and control policies, the problem can be formulated as a tractable convex optimization problem. We show that our framework captures several families of (convex) uncertainty sets of practical interest, and illustrate our approach on a demand response problem of providing control reserves for a power system.