Quadratic Performance Index Research Articles

Intelligent optimal hybrid motion/force control of constrained robot manipulator

This paper presents a neural network-based optimal control approach for hybrid motion/force control problem of robot manipulators in the presence of structured and unstructured uncertainties. The quadratic optimisation with sliding mode control and neural network is utilised to propose an optimal hybrid motion/force control of robotic manipulators. Firstly, the dynamics of robot manipulator is reduced into state-space form describing the constrained and unconstrained motion separately. Then the optimal hybrid motion/force control scheme is derived utilising the optimisation of Hamilton Jacobi Bellman (HJB) equation and sliding mode control approach. The structured and unstructured uncertainties of the system are compensated using radial basis function neural network and adaptive compensator. The radial basis function neural network approximates the unknown dynamics and adaptive compensator is used to estimate the bounds on neural network approximation error and the unstructured uncertainties of the system. The neural networks are trained in online manner using weight update algorithms derived with Lyapunov approach to guarantee the tracking stability and error convergence with prescribed quadratic performance index. Finally, the proposed control approach is verified through simulation results with two link constrained manipulator in a comparative manner.

Parametric variational procedure to solve index-3 semi explicit linear-regulator control problem with constrained robot illustration

The aim of this work is to solve 2-dimensional, 3-links linearized constrained robot problem. This problem is of index-three linear descriptor control problem. Since the aim is to regulate its output, a quadratic performance index is proposed to form an index-3 linear regulator optimal control problem. Firstly, the problem has been transformed into standard constrained optimal control problem over class of consistent initial condition with solvability assumptions. Secondly, the solution of differential-algebraic equation has been shown as equivalent to find the critical points of some variational formulation and vise- versa. Then aggregating all functional (performance one) with consistent initial conditions in one performance (weighted) index. Under standard topology of the solvability, a parametric approach has been proposed to approximate the state-space solutions with control over the class of constraints. Hence, an infinite dimensional problem is transformed into finite one, and then an approximate solutions is obtained by solving the class of linear algebraic equations. The proposed approach is easily implemented and accurate up to decision maker selections of the parameterization basis functions and their numbers.

Application of periodic Bernoulli polynomials in approximating the solution of linear time-delay optimal control problems

In this paper, a numerical method based on application of periodic Bernoulli polynomials for solving optimal control of linear time-delay systems with quadratic performance index is presented. Some important properties of Bernoulli polynomials are reviewed and a new operational matrix of delay based on these functions is introduced. Also an error bound for approximating a function with periodic Bernoulli polynomials is presented. Using operational matrices of differentiation, delay and the integration of the cross product of two Bernoulli polynomials, the linear time delay optimal control problem with quadratic objective function is converted to a nonlinear optimization problem. Finally, numerous illustrative examples are studied to show the efficiency and accuracy of the proposed method compared with some other methods.

Asymmetric information control for stochastic systems with different intermittent observations

This paper will investigate the linear quadratic (LQ) control problem for a stochastic system with different intermittent observations. Different from traditional LQ control problems, two controllers with different information structures are considered to minimize a quadratic performance index. Specifically, the information sets available to two controllers are different and mutually exclusive (i.e., either of both is not the subset of the other one). The problem under consideration in this paper is an asymmetric information control problem. It is highlighted that previous literature on asymmetric information control mainly focused on the case when the information set is a subset of the other one. However, the case of the information sets being mutually exclusive remains less investigated to the best of our knowledge, which brings essential difficulties in finding the optimal control strategies: the structures and forms of two controllers are not clear; seeking for the solvability conditions of the optimal control problem is challenging. We summarize the contributions of this paper as follows: Firstly, by adopting the convex variational method, the necessary and sufficient solvability conditions are derived under some basic assumptions, which are relied on the forward and backward difference equations (FBSDEs); Secondly, by decoupling the FBSDEs, the control strategies are derived; Finally, the results are extended to investigate the general multiple controllers case.

Optimum Value based under Voltage Load Shedding Strategies

ABSTRACT This paper presents a novel technique for optimum load shedding in a power system based on under voltage considerations. A quadratic performance index based on voltage deviation has been adopted. The value of performance index may be adjusted based on the corrected voltage after load shed. Hence load shed depends on the desired bus voltage after load shed. Thus implicitly a value based load shed have been obtained which a utility may use. All operating constraints have been considered using load flow program. Formulated optimization problem has been solved by employing three Rao’s metaphor-less algorithms. Statistical inference have been provided and results obtained on IEEE 14-bus sample test system have been compared with those obtained using EPSDE (Differential Evolution Algorithm with Ensemble of Parameters and Mutation Strategies) algorithm which is an important variation of differential algorithm.

Design of nonlinear optimal tracking control law based on finite-time stability for quadratic performance index

In this paper, a design method of optimal tracking control based on finite-time stability for quadratic performance index is proposed. Finite-time stability of tracking control involves dynamical systems whose actual output can track desired output in finite time while satisfying Lyapunov stability. A nonlinear control law which guaranteed finite-time stability is designed depending on the core idea of dynamic programming. By using Hamilton–Jacobi–Bellman (HJB) equation and finite-time stability theory, sufficient conditions involving V-function are provided, and design steps for nonlinear finite-time tracking control law are derived by constructing augmented systems. In addition, the V-function is constructed to obtain corresponding law for given systems, which verified that the design method is feasible. Simulation examples validate the efficiency of the results.

Design of an Optimal Variable Structure Controller for Electromechanical Systems.(Dept.E)

A control design technique based on the theory of variable structure (VSS) is proposed. The proposed technique is developed for designing an optimal model following adaptive controller, for an electromechanical system. The model that specifies the design objectives is a part of the system. A systematic procedure for the selection of the switching hyperplanes in the design of the optimal variable structure controller is developed, by minimizing a quadratic performance index in the sliding mode operation. The design procedures describes and the results on a simulation study is presented, showing the effectiveness of the designed controller under the effect of disturbances.

Two novel approaches to capture the maximum power from variable speed wind turbines using optimal fractional high-order fast terminal sliding mode control

In this paper, two nonlinear control approaches using optimal fractional high-order fast terminal sliding mode (FHOFTSM) control are proposed to maximize the captured wind energy and minimize the mechanical loads in the variable speed wind turbines (VSWTs). The optimal condition of the system which uses the presented approaches is achieved by creating a compromise between maximizing the energy extraction and minimizing the control input. So, the mechanical stress on the drive-train is reduced by minimizing the control input. To achieve this compromise, the behavior of the wind turbine system should be precisely modeled. Fractional calculus theory is an effective method for modeling the VSWT, which provides a more accurate description of the system performance compared with integer-order modeling. Based on the fractional-order modeling of the system, the optimal approach is designed by calculating the error dynamics of the system and defining two types of performance indexes, integer-order and fractional-order performance indexes. Hence, the design procedure of an optimal FHOFTSM control for each performance index requires two-stages process. At first phase, an optimal controller is presented for the system nominal error to minimize the quadratic performance index. Then a switching controller is offered in the second phase that is obtained by defining the fractional high-order sliding manifold and fractional nonsingular fast terminal sliding manifold to overcome the unknown disturbance. Hence, the order of the controllers is smaller than the second order. The optimal strategy is applied to minimize the control input, whereas the FHOFTSM method is used to obtain the maximum wind power extraction, reduce mechanical loads, attenuate the chattering, and achieve fast finite-time convergence. The closed-loop stability of the control system is approved by the fractional Lyapunov direct method and the Mittag-Leffler stability theorem. To illustrate the effectiveness of the proposed approaches, the proposed controllers are compared with some already existing controllers. The performance of controllers is verified through three scenarios, i.e., random variation of wind speed, step change of wind speed, and robustness against parameter uncertainties, in which the simulation results confirm the effectiveness of the proposed controllers.

Optimal Output Synchronization Control of a Class of Complex Dynamical Networks With Partially Unknown System Dynamics

This paper is concerned with the optimal output synchronization control problem for a class of heterogeneous complex dynamical networks (CDNs) with partially unknown system dynamics. By defining a new quadratic performance index including the information of state couplings, an optimal controller consisting of a feedback control and a compensated feedforward control is then designed. A necessary and sufficient condition for the optimal control minimizing the quadratic performance index is established. Especially, an algebraic Riccati equation (ARE) associated with a discount factor is obtained, and a novel online iteration algorithm by iteratively solving the ARE is proposed to compute the optimal controller gain for the case that the CDNs are with partially unknown system dynamics. Moreover, it is proved that the output synchronization errors converge to zero asymptotically by applying the optimal control laws. Finally, two simulation examples are provided to verify the effectiveness of the proposed control method.

Learning and Near-Optimal Control of Underactuated Surface Vessels With Periodic Disturbances.

In this article, we propose a novel learning and near-optimal control approach for underactuated surface (USV) vessels with unknown mismatched periodic external disturbances and unknown hydrodynamic parameters. Given a prior knowledge of the periods of the disturbances, an analytical near-optimal control law is derived through the approximation of the integral-type quadratic performance index with respect to the tracking error, where the equivalent unknown parameters are generated online by an auxiliary system that can learn the dynamics of the controlled system. It is proved that the state differences between the auxiliary system and the corresponding controlled USV vessel are globally asymptotically convergent to zero. Besides, the approach theoretically guarantees asymptotic optimality of the performance index. The efficacy of the method is demonstrated via simulations based on the real parameters of an USV vessel.

Dynamic modelling and linear quadratic sliding mode control of a multivariable looper system in hot strip mills

This paper introduces a linear quadratic sliding mode control (LQ-SMC) scheme into a looper control system. First, according to a 1700 mm tandem hot mill, the state-space dynamic model of the looper system was established, and then, the optimal control law of the looper system was obtained based on the established model. Finally, the optimal sliding mode and optimal sliding mode control law of the LQ-SMC scheme were designed such that the sliding motion could satisfy the optimal value of the quadratic performance index. Simulation results show that the proposed control scheme has complete robustness to external disturbances that satisfies certain conditions, and the coupling between the looper angle dynamic and strip tension dynamic is also minimized.

Multi-Objective Optimal Control for Uncertain Singularly Perturbed Systems

This paper studies the passive multi-objective optimal control of uncertain singularly perturbed systems. First, the uncertainty is described in a norm-bounded way, and then the state space model of the system is determined. Further time, the problem of passivity can also be transformed into a linear quadratic performance index problem. According to the Lyapunov stability theory, the system robust stability criterion is derived, based on the above conclusion, the corresponding parameterized passive multi-objective controller is designed using state feedback, and the weight matrix and the minimum performance index are solved based on the optimal control theory. Finally, a numerical example is given to illustrate the correctness and feasibility of the control method.

Application of Adaptive Control on Carbon Fiber Diagonal Loom

In order to improve the control effect of the tension fluctuation, a single neuron adaptive control strategy based on quadratic performance index is proposed in this paper. The structure and the working principle of carbon fiber diagonal loom are studied which can be used for dynamic analysis and controller design. With the idea of optimal control, the parameters of the controller are adjusted by minimizing the sum of the square of the output error and the control increment. The simulation results based on TrueTime show that the strategy adopted in this paper compared with the traditional control strategy have the advantages of faster response time and smaller overshoot in networked control system.

Lyapunov Redesign for Input and State Delays Systems by Using Optimal Predictive Control and Ultimate Bound Approaches: Theory and Experiments

This article deals with the robust control design for linear systems with input and state delays, subject to nonvanishing matched disturbances. The controller is synthesized with the Lyapunov redesign technique in two stages: first, an optimal predictor compensates the input delay of the nominal system while a quadratic performance index is minimized. Then, the robust component guarantees that the solutions are ultimately bounded. The theoretical results are experimentally validated through a dehydration process, with the controller digital implementation on an industrial programmable automation controller cDAQ-9132.

Corresponding drivability control and energy control strategy in uninterrupted multi-speed mining trucks

An hybrid uninterrupted multi-speed transmission (HUMST), based on the integration of a planetary gear set and a 3-speed automatic manual transmission (3-AMT), is developed to satisfy the specific performance indexes of mining trucks. The power-split device can alleviate and eliminate the inherent torque interruption of the 3-AMT during gear shift by implementing the designed cooperative shift control strategy which is optimized by quadratic performance index. In order to achieve fast torque coordination while guaranteeing the driving comfort performance, the torque profiles of the power split device and the traction motor are optimized by Linear-quadratic regulator (LQR) algorithm. Dynamic programming (DP) is implemented as a benchmark to demonstrate the maximum fuel efficiency of the proposed HUMST. Because of the high computational cost of optimal control strategies such as DP, an improved real-time control strategy (IRTCS) using modified Gaussian distribution function is proposed to significantly reduce the computing load. As efficiency-oriented energy control strategy would result in frequent gear shifts, to achieve a desirable tradeoff between the overall efficiency and the shift stability, multi-objective genetic algorithm (MGA) is integrated to optimize the overall performance. The detail mathematical and dynamic model shows that the proposed shifting strategy with LQR can effectively suppress shift jerk, and the proposed IRTCS with MGA can reduce shift frequency by 70.78% to improve the drivability, only sacrificing 4.86% of overall efficiency compared to that of DP.

Optimal distributed cooperative control for multi-agent systems with constrains on convergence speed and control input

This paper focuses on the distributed optimal cooperative control for multi-agent systems (MASs) over fixed communication graphs. Firstly, it is proved that the optimal distributed control for the local quadratic performance indexes of all agents is equivalent to solve a globally optimal problem, the resulting optimal Laplacian matrix associates with a complete graph hence the optimal distributed protocols do not exist. Consequently, we turn to solve the globally optimal distributed control problem for the candidate protocols with specified distributed structure. Furthermore, suboptimal fully distributed protocols can be designed when the Laplacian matrix and the initial states of all agents are unavailable. As a simple application, the minimum energy distributed cooperative control problem is addressed. Then, from a practical viewpoint, we solve the distributed optimal control problem with constrains on specified convergence speed and control input. Sufficient conditions for existence of the optimal solutions are derived. Finally, simulation examples are given to verify the effectiveness of the proposed results.

Autonomous Vehicle Convoy Formation Control with Size/Shape Switching for Automated Highways

Today’s semi-autonomous vehicles are gradually moving towards full autonomy. This transition requires developing effective control algorithms for handing complex autonomous tasks. Driving as a group of vehicles, referred to as a convoy, on automated highways is a highly important and challenging task that autonomous driving systems must deal with. This paper considers the control problem of a vehicle convoy modeled with linear dynamics. The convoy formation requirement is presented in terms of a quadratic performance index to minimize. The convoy formation control is formulated as a receding horizon linear-quadratic (LQ) optimal control problem. The receding horizon control law is innovatively defined via the solution to the algebraic Riccati equation. The solution matrix and therefore the receding horizon control law are obtained in the closed-form. A control architecture consisting of four algorithms is proposed to handle formation size/shape switching. The closed-form control law is at the core of these algorithms. Simulation results are provided to justify the models, solutions, and proposed algorithms.

Active Vehicle Suspension with Anti-Roll System Based on Advanced Sliding Mode Controller

In the paper authors consider the active suspension of the wheeled vehicle. The proposed controller consists of a sliding mode controller used to roll reduction and linear regulators with quadratic performance index (LQRs) for struts control was shown. The energy consumption optimization was taken into account at the stage of strut controllers synthesis. The studied system is half of the active vehicle suspension using hydraulic actuators to increase the ride comfort and keeping safety. Instead of installing additional actuators in the form of active anti-roll bars, it has been decided to expand the active suspension control algorithm by adding extra functionality that accounts for the roll. The suggested algorithm synthesis method is based on the object decomposition into two subsystems whose controllers can be synthesized separately. Individual suspension struts are controlled by actuators that use the controllers whose parameters have been calculated with the LQR method. The mathematical model of the actuator applied in the work takes into account its nonlinear nature and the dynamics of the servovalve. The simulation tests of the built active suspension control system have been performed. In the proposed solution, the vertical displacements caused by uneven road surface are reduced by controllers related directly to suspension strut actuators.

Optimal Clutch Pressure Control in Shifting Process of Automatic Transmission for Heavy-Duty Mining Trucks

The optimal control of automatic transmission plays an important role in the shifting smoothness and fuel economy of heavy-duty mining trucks. In this paper, a dynamic model of the powertrain system is built to study the clutch pressure control during the shifting process. A linear-quadratic optimal regulator is used to achieve the optimum control pressure of clutches, where shifting jerk and clutch friction loss are chosen to a form quadratic performance index function. Besides, a detailed solution of the linear-quadratic problem with the disturbance matrix in the state equations is provided. This paper also carries out a software simulation and verification of the normal condition (no load without slope) and the extreme condition (full load with maximum slope). Compared with the preset reference trajectory control, the simulation results show that the proposed optimal clutch pressure control can effectively reduce jerk and friction loss during the shifting process and has good robustness to different operating conditions.

Finite horizon nonlinear optimal control for a quadrotor: Experimental results

SummaryIn this article, a suboptimal nonlinear discrete control sequence for nonlinear discrete affine control systems is proposed. Using the dynamic programming approach in discrete time domain, the suboptimal control sequence is obtained in every step considering a quadratic performance index of finite horizon. The proposed control strategy is applied to improve the dynamic and energetic performances of a quadrotor unmanned aerial vehicle, when it is subject to special maneuvers or flight conditions, such as the take off and landing phases or trajectory tracking. For these tasks, it could be required convergence in finite time and good behavior. Performing a comparative experimental study with others controllers (optimal linear and PD controllers), the effectiveness of proposed approach is proven.