Linear Quadratic Objective Function Research Articles

Adaptive model predictive control design using multiple model second level adaptation for parameter estimation of two‐degree freedom of helicopter model

AbstractThis paper proposed an adaptive nonlinear model predictive control approach for a 2‐DoF helicopter model with both parametric uncertainties and input–output constraints. In the proposed control technique, the nonlinear helicopter model is linearized along the prediction horizon using a state and parameter‐dependent state‐space model. Furthermore, a linear quadratic objective function with constraints is carried out using the developed linearized model. Here, the multiple estimation model and the concept of second‐level adaptation are used to handle the parametric uncertainty of the nonlinear system. To ensure the boundedness of the estimated parameter within a predefined compact region, a projection based adaptive law is used. The adaptive tuning laws for the unknown parameters are derived by Lyapunov stability analysis. An ensemble Kalman filter has been used to observe the unavailable states of the 2‐DoF helicopter model. The effectiveness of the proposed control algorithm has been verified successfully in simulation as well as real‐time experimental setup of 2‐DoF of helicopter model and results are documented in tabular form to show superiority with an existing approach.

Long-step path-following algorithm for solving symmetric programming problems with nonlinear objective functions

We developed a long-step path-following algorithm for a class of symmetric programming problems with nonlinear convex objective functions. The theoretical framework is developed for functions compatible in the sense of Nesterov and Nemirovski with $$-\,\ln \det $$ barrier function. Complexity estimates similar to the case of a linear-quadratic objective function are established, which gives an upper bound for the total number of Newton steps. The theoretical scheme is implemented for a class of spectral objective functions which includes the case of quantum (von Neumann) entropy objective function, important from the point of view of applications. We explicitly compare our numerical results with the only known competitor.

The choice of a growth path under a linear quadratic approximation

There is a recent strand of literature which suggests that second order approximations of linear quadratic objective functions in the steady state vicinity, namely when assuming stochastic scenarios, lead to very interesting and useful results. For example, applications in monetary policy resort to such technique. In this paper we find that, for a specific optimal control problem under a purely deterministic setup, a second-order approximation of the objective function may lead to inaccurate results, particularly when one considers exogenous variables as arguments of the objective function. These results are related to the stability conditions, which in the present case can be written as constraints to a discount rate associated with future outcomes. We designate the proposed model as an ‘optimal growth control’ model, from which we compute general conditions about stability and analyse the application of such a framework to a fertility - human capital problem.

Quality and uniformity control of fiber web by roller card system. Part II: Design and validation of a roller card control system

Thin web is produced from flocks of raw fiber after being processed by a carding system. In the conventional carding machine, the multi-roller design of the system has dynamic characteristic of time delay, and the quality of web output evenness is affected by the control methods. Based on the new mathematical model of a carding machine, this paper employed a new carding control system and fiber optic sensor to establish a new carding control system. The proposed improved model predictive controller is developed to solve the problem of time delay in the roller carding system using a discrete state and linear quadratic objective function, in order to minimize the deviation between predictive output and given target value. The designed controller is compared with the proportional plus integral (PI) controller based on the conventional control theories and state feedback integral controller using modern control theories as well. In experimental verification, the fiber optic sensor is installed to measure web output at the doffer, a feeding roller is controlled to change the feeding of raw cotton. The results confirm that the proposed improved model predictive controller can be provided not only to enable the output response reach the control objects also improve the production efficiency of the carding machine and enhance the web output evenness.

Constrained output feedback model predictive control for nonlinear systems

A constrained output feedback model predictive control approach for nonlinear systems is presented in this paper. The state variables are observed using an unscented Kalman filter, which offers some advantages over an extended Kalman filter. A nonlinear dynamic model of the system, considered in this investigation, is developed considering all possible effective elements. The model is then adaptively linearized along the prediction horizon using a state-dependent state space representation. In order to improve the performance of the control system as many linearized models as the number of prediction horizons are obtained at each sample time. The optimum results of the previous sample time are utilized for linearization at the current sample time. Subsequently, a linear quadratic objective function with constraints is formulated using the developed governing equations of the plant. The performance and effectiveness of the proposed control approach is validated both in simulation and through real-time experimentation using a constrained highly nonlinear aerodynamic test rig, a twin rotor MIMO system (TRMS).

Stable model predictive control for a nonlinear system

In this paper, a stable model predictive control approach is proposed for constrained highly nonlinear systems. The technique is a modification of the multistep Newton-type control strategy, which was introduced by Li and Biegler. The proposed control technique is applied on a constrained highly nonlinear aerodynamic test bed, the twin rotor MIMO system (TRMS) to show the efficacy of the control technique. Since the accuracy of the plant model is vital in MPC techniques, the nonlinear state space equations of the system are derived considering all possible effective components. The nonlinear model is adaptively linearized during the prediction horizon. The linearized models of the system are employed to form a linear quadratic objective function subject to a set of inequality constraints due to the system input/output limits. The stability of the control system is guaranteed using the terminal equality constraints technique. The satisfactory performance of the proposed control algorithm on the TRMS validates the effectiveness and the reliability of the approach.

Observer-based robust model predictive control of singular systems

The robust model predictive control problem is studied for the singular systems with norm-bounded uncertainties when the states of controlled systems are immeasurable. By constructing the Lyapunov function with the error terms, the observer-based feedback control law is calculated by minimising the worst-case linear quadratic objective function. At each sampling time, the sufficient conditions for the existence of robust model predictive control are derived and expressed as linear matrix inequalities. It is proved that the robust stability of the closed-loop singular systems is guaranteed when the obtained feedback controller satisfies some conditions, and the regular and the impulse-free of the singular systems are also guaranteed. A simulation example is give to illustrate the efficiency of this method.

Dynamic Modeling and Optimal Controller Design of a Spherical Robot in Climbing State

Spherical robot is a kind of mobile robot, and then it is inevitable to encounter with the problem of climbing slope. According to the spherical robot designed, each independent variable describing the state of climbing an arbitrary slope is analyzed. The calculation formula to estimate climbing capability is given and simultaneously the concept of critical pendulum angle is proposed. Dynamic equations of the robot climbing slope is derived from using Lagrangian function equation based on energy dissipation. In order to solve the problem of constant terms in the equation, the coordinate transformation method is adopted, and ultimately the system is converted into state-space form. When every state of the robot system can be measured, a corresponding linear quadratic objective function is designed with the consideration of the practical requirements of both steady movement and less energy assumption. At last, the state feedback matrix is designed, which can control the robot to move at an expected velocity on slope, and the simulation results prove the validity of the above control technique.

Robust Model Predictive Control of Singular Systems

This note is concerned with model predictive control for linear singular systems with time-varying uncertainties. A piecewise constant control sequence is calculated by minimizing the worst-case linear quadratic objective function. At each sample time, the sufficient conditions on the existence of the model predictive control are derived and expressed as linear matrix inequalities. The robust stability of the closed-loop systems is guaranteed by the proposed design method.

Modified Sliding Mode Control for Wind-Excited Benchmark Problem

Among promising control strategies, the sliding mode control is particularly robust with respect to structural uncertainty. In this paper, a modified sliding mode control (MSMC) strategy using dynamic output feedback is presented and demonstrated for the wind-excited benchmark building equipped with an ATMD (active tuned mass damper) control device. The main advantage of the MSMC presented is its ability to systematically modulate the control effort through the introduction of a prefilter prior to the control force. For practical implementation of a MSMC using acceleration measurements at strategic locations, a Kalman.Bucy filter type of observer is designed based on the augmented system. Hence the sliding surface design is composed of the observer state, and the modulation of control forces can be achieved by forming an optimization problem with a linear quadratic objective function. As shown by the simulation results of the wind-excited benchmark building, the modified sliding mode controller indeed has the capability of systematically modulating the control force. Moreover, the remarkable performance of the MSMC demonstrates that the strategy presented is suitable for the wind-excited tall buildings.