Nonlinear State Dependent Riccati Equation Research Articles

Finite-time integral fast terminal sliding mode control for uncertain quadrotor UAV based on state-dependent Riccati equation observer subjected to disturbances

This paper presents a new control approach of trajectory tracking for quadrotor unmanned aerial vehicle (UAV) systems under external disturbances and parameter uncertainties. The integral fast terminal sliding mode control (IFTSMC) approach applying state-dependent Riccati equation (SDRE) observer is presented for this purpose. As a result, the nonlinear SDRE observer is designed to estimate the non-measurable states. Afterward, employing the estimated states of the SDRE observer, the proposed IFTSMC controller is designed for trajectory tracking of the perturbed quadrotor UAV. Besides, applying Lyapunov’s stability theory, the finite-time convergence and robustness of the closed-loop UAV system are assured. Based on the numerical simulation results, the proposed controller successfully tracked various reference trajectories of quadrotor UAVs despite external disturbances and parametric uncertainty.

Nonlinear State Dependent Riccati Equation Controller for 3-DOF Airfoil with Cubic Structural Nonlinearity

In this paper, Limit Cycle Oscillations (LCOs) of a Two-Dimensional (2-D) airfoil with cubic structural nonlinearity in the plunge Degree of Freedom (DOF) are investigated. The aerodynamic loads are modelled using the unsteady Theodorsen’s theory. Wagner function and Jones’ approximation are used to transform the unsteady aerodynamic loads from frequency domain into time domain. The aeroelastic differential equations are solved using the routine ODE45 in MATLAB to get the system response. Both subcritical and supercritical LCOs are observed in the 3-DOF airfoil with structural nonlinearity in the plunge DOF. Such LCOs are undesirable phenomena and should be suppressed within the flight envelope. A nonlinear state feedback controller is designed to minimize the amplitude of LCOs presented in the considered nonlinear aeroelastic system. The State-Dependent Riccati Equation (SDRE) approach in combination with Kalman filter technique is used to design a controller for the 2-D airfoil with trailing edge control surface (flap). The forces and moments produced by this flap’s action are used to stabilize the system and suppress the existence of LCOs. The efficiency of the proposed nonlinear controller by the SDRE and Kalman filter in suppressing the existence of subcritical and supercritical LCOs are verified by the numerical simulation results.

Nonlinear SDRE based adaptive fuzzy control approach for age-specific drug delivery in mixed chemotherapy and immunotherapy

Determination of a near-optimal personalized drug delivery scenario in mixed chemotherapy and immunotherapy based on the age of cancer patients was presented in this paper. For this purpose, a mathematical model for cancer dynamics is considered in the form of ordinary differential equations (ODE) which contains cancer cells, tumor cells, and chemotherapy drug intervention. This model is modified by adding immunotherapy intervention effects to alter cancer dynamics. We consider two patients with known and unknown model parameters which are mentioned as a reference and unknown patients respectively. The nonlinear composite adaptive controller is introduced by compounding State Dependent Riccati Equation (SDRE) and Model Reference Adaptive Control (MRAC) techniques for achieving the drug delivery of an unknown patient. The drug delivery scenario for a reference patient with a known mathematical model and parameters is determined via the SDRE technique and then for any unknown patient, the personalized mixed therapy protocol is achieved using the treatment regimen of the reference patient as a reference model in MRAC. To reduce the side effects of chemotherapy drugs, we determine drug maximum dose limits using fuzzy control by considering the age of cancer patients. We regarded patients in four age groups of child, young, middle-aged, and old. In the proposed methodology, unknown patients are considered as a black-box simulator and the mathematical model parameters of the patient are not essential for the design of drug administration protocol and we only need patients’ age. After chemotherapy, the treatment is completed by immunotherapy to avoid cancer relapse. The effect of reference and unknown patient ages in obtaining drug delivery protocol is deeply surveyed. Numerical simulations confirm the effectiveness, robustness, and flexibility of the proposed strategy for patients of different ages. The Proposed algorithm can be an effective tool to aid oncologists in prescribing age-specific optimal treatment protocols for cancer patients.

Attitude coordination of multiple spacecraft for space debris surveillance

This paper discusses the attitude coordination of a formation of multiple spacecraft for space debris surveillance. Off-the-shelf optical sensors and reaction wheels, with limited field of view and control torque, respectively, are considered to be used onboard the spacecraft for performing the required attitude maneuvers to detect and track space debris. The sequence of attitude commands are planned by a proposed algorithm, which allows for a dynamic team formation, as well as performing suitable maneuvers to eventually point towards the same debris. A control scheme based on the nonlinear state dependent Riccati equation is designed and applied to the space debris surveillance mission scenario, and its performance is compared with those of the classic linear quadratic regulator and quaternion feedback proportional derivative controllers. The viability and performance of the coordination algorithm and the controllers are validated through numerical simulations.

Modeling and nonlinear control of a flexible-link manipulator

The problem of modeling and controlling the tip position of a one-link flexible manipulator is considered. The proposed model has been used to investigate the effect of the open-loop control torque profile, and the payload. The control strategy is based on the nonlinear State Dependent Riccati Equation (SDRE) design method in the context of application to robotics and manufacturing systems. In this paper, an experimental test-bed was developed to demonstrate the concept of end-point position feedback on a single-link elastic manipulator, and the control strategy for a single-link flexible manipulator. The controller is designed based on the nonlinear SDRE developed by the authors and applied to a flexible manipulator. The experimental results are compared with conventional PD controller strategy. The results reveal that the nonlinear SDRE controller is near optimal and robustly; and its performance is improved comparing to the PD control scheme.

SDRE CONTROL OF THE CONTROL ACTUATION SYSTEM OF A GUIDED MISSILE

This article illustrates the design and analysis of a nonlinear State-Dependent Riccati Equation (SDRE) controller on a control actuation system (CAS) of an aerodynamically controlled guided missile. The system consists of a DC-motor, the transmission mechanism, a control actuation surface (fin), and a position feedback device. The overall system has to satisfy the desired performance requirements in the presence of the nonlinear modeling characteristics: aerodynamic loading and backlash in the transmission mechanism, both of which are unknown to the controller. Moreover, there are uncertainties in DC-motor parameters and supplied power. The use of a state-dependent (nonquadratic) performance functional is strongly emphasized for control design purposes to show how the integration of mathematical synthesis and engineering objectives can be achieved. A series of numerical simulations are carried out to evaluate the effectiveness and robustness of the proposed nonlinear SDRE controller.

Controllability Issues in Nonlinear State-Dependent Riccati Equation Control

Inthelastfewyears,algorithmsusingstate-dependentRiccatiequations (SDREs)havebeenproposedforsolving nonlinear control problems. Under state feedback, pointwise solutions of an SDRE must be obtained along the system trajectory. To ensure the control is well dee ned, global controllability and observability of state-dependent system factorizations are commonly assumed. Here connections between controllability of the state-dependent factorizations and truesystem controllability are rigorously established. Itisshown thata localequivalencealways holdsfortheclassofsystemsconsidered,andspecialcasesthatimplyglobalequivalencearealsogiven.Additionally, a notion of nonlinear stabilizability is introduced, which is a necessary condition for global closed-loop stability. The theory is illustrated by application to a e ve-state nonlinear model of a dual-spin spacecraft.