On design of suboptimal tracking controller for a class of nonlinear systems

Batmani, Yazdan; Davoodi, Mohammadreza; Meskin, Nader

doi:10.1109/acc.2016.7525061

Cited by 11 publications

(27 citation statements)

References 25 publications

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“…In this section, using the proposed SDRE technique in , an event‐triggered tracking controller is developed to solve the optimal trajectory tracking problem defined in Subsection 2.2. The main results of this proposed event‐triggered algorithm, called the event‐triggered SDRE tracking controller, are represented in the following theorem.…”

Section: Event‐triggered Controller Design Methodologymentioning

confidence: 99%

“…By defining

U (t) = e^{- γ t} u (t), X (t) = e^{- γ t} 1.19em [x^{normalT} (t) x_{normald}^{normalT} (t) {1.19em]}^{normalT}

, and using the SDC representations f ( x ( t ))= F ( x ( t )) x ( t ), h ( x ( t ))= H ( x ( t )) x ( t ), f d ( x d ( t ))= F d ( x d ( t )) x d ( t ), and h d ( x d ( t ))= H d ( x d ( t )) x d ( t ), the optimal tracking problem defined in Subsection 2.2 is converted to an optimal regulation one with the following infinite‐time quadratic cost function :

\begin{matrix} right J (X_{0}, U (t)) = \frac{1}{2} \int_{0}^{\infty} (() & left X^{T} (t) Q (e^{γ t} X (t)) X (t) & right \\ right & left + U^{T} (t) R U (t) ()) d t, \end{matrix}

and the dynamics of the augmented state X ( t ) is as follows :

\begin{matrix} right \dot{X} (t) & left = (() - γ I + [\begin{matrix} F (x (t)) & 0 \\ 0 & F_{normald} (x_{normald} (t)) \end{matrix}] ()) X (t) & right \\ right & left + [] \end{matrix}

…”

Section: Event‐triggered Controller Design Methodologymentioning

confidence: 99%

“…x d (t), and h d (x d (t)) = H d (x d (t))x d (t), the optimal tracking problem defined in Subsection 2.2 is converted to an optimal regulation one with the following infinite-time quadratic cost function [16,22]:…”

Section: F(x(t))x(t) H(x(t)) = H(x(t))x(t) F D (X D (T)) = F D (X Dmentioning

confidence: 99%

“…) is assumed to be point-wise stabilizable and point-wise detectable, it is possible to apply the event-triggered SDRE regulator, proposed in Subsection 3.1, to the latter optimal problem (15) and (16). Using the results of Theorem 1, one can conclude that the augmented state X (t) asymptotically tends to zero under the control law (14).…”

Section: F(x(t))x(t) H(x(t)) = H(x(t))x(t) F D (X D (T)) = F D (X Dmentioning

confidence: 99%

“…The state‐dependent Riccati equation (SDRE) techniques were developed to solve many different control engineering problems in some broad classes of nonlinear systems . The key idea behind an SDRE technique is in representing the nonlinear system dynamics as a state‐dependent linear system which is called the pseudo linearization, extended linearization, and/or state‐dependent coefficient (SDC) matrix representation .…”

Section: Introductionmentioning

confidence: 99%

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On the Design of Event‐Triggered Suboptimal Controllers for Nonlinear Systems

Batmani

2017

Asian Journal of Control

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In this paper, two suboptimal event-triggered control techniques are proposed for both the regulation and the tracking problems in a broad class of nonlinear networked control systems. The proposed techniques are based on the state-dependent Riccati equation (SDRE) methodology. In the case of the regulation problem, the asymptotic stability of the origin of the closed-loop system under the proposed event-triggered control law is investigated. In addition, for the tracking problem, it is proved that the tracking error between the system output and its desired trajectory converges asymptotically to zero under some mild conditions. It is shown that the proposed methods can considerably reduce the information exchange between the controller and the actuator. Due to the implementation procedures of the proposed techniques, no Zeno behavior is occurred. Three numerical simulations are provided to demonstrate the design procedure and the flexibility of the proposed event-triggered control techniques.

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Section: Event‐triggered Controller Design Methodologymentioning

confidence: 99%

“…By defining

U (t) = e^{- γ t} u (t), X (t) = e^{- γ t} 1.19em [x^{normalT} (t) x_{normald}^{normalT} (t) {1.19em]}^{normalT}

\begin{matrix} right J (X_{0}, U (t)) = \frac{1}{2} \int_{0}^{\infty} (() & left X^{T} (t) Q (e^{γ t} X (t)) X (t) & right \\ right & left + U^{T} (t) R U (t) ()) d t, \end{matrix}

and the dynamics of the augmented state X ( t ) is as follows :

\begin{matrix} right \dot{X} (t) & left = (() - γ I + [\begin{matrix} F (x (t)) & 0 \\ 0 & F_{normald} (x_{normald} (t)) \end{matrix}] ()) X (t) & right \\ right & left + [] \end{matrix}

…”

Section: Event‐triggered Controller Design Methodologymentioning

confidence: 99%

Section: F(x(t))x(t) H(x(t)) = H(x(t))x(t) F D (X D (T)) = F D (X Dmentioning

confidence: 99%

Section: F(x(t))x(t) H(x(t)) = H(x(t))x(t) F D (X D (T)) = F D (X Dmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the Design of Event‐Triggered Suboptimal Controllers for Nonlinear Systems

Batmani

2017

Asian Journal of Control

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Gravity compensation and optimal control of actuated multibody system dynamics

Nekoo

Acosta

Ollero

2021

IET Control Theory & Appl

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This work investigates the gravity compensation topic, from a control perspective. The gravity could be levelled by a compensating mechanical system or in the control law, such as proportional derivative (PD) plus gravity, sliding mode control, or computed torque method. The gravity compensation term is missing in linear and nonlinear optimal control, in both continuous-and discrete-time domains. The equilibrium point of the control system is usually zero and this makes it impossible to perform regulation when the desired condition is not set at origin or in other cases, where the gravity vector is not zero at the equilibrium point. The system needs a steady-state input signal to compensate for the gravity in those conditions. The stability proof of the gravity compensated control law based on nonlinear optimal control and the corresponding deviation from optimality, with proof, are introduced in this work. The same concept exists in discrete-time control since it uses analog to digital conversion of the system and that includes the gravity vector of the system. The simulation results highlight two important cases, a robotic manipulator and a tilted-rotor hexacopter, as an application to the claimed theoretical statements.

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Design an omnidirectional autonomous mobile robot based on non‐linear optimal control to track a specified path

Shahgholian,

Akhavan,

Kamrani

et al. 2024

IET Control Theory & Appl

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This paper explores two non‐linear control techniques for designing an effective control system for an omnidirectional autonomous mobile robot with four Mecanum wheels. Due to the unique wheel structure and four separate wheels, the robot has non‐linear dynamics, multiple inputs and outputs. The first technique uses the state‐dependent Riccati equation (SDRE) to address optimal non‐linear control while considering energy and time constraints. The second technique, using an intermediate variable , has expanded the Hamilton‐Jacobi‐Belman equation in terms of the power series. Consequently, these equations are reduced to a set of recursive Lyapunov algebraic equations, leading to a closed‐form solution for solving the non‐linear optimal control problem. Finally, the maneuverability and path‐tracking capability of the robot are examined by highlighting the non‐linear term through numerical simulation.

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On design of suboptimal tracking controller for a class of nonlinear systems

Cited by 11 publications

References 25 publications

On the Design of Event‐Triggered Suboptimal Controllers for Nonlinear Systems

On the Design of Event‐Triggered Suboptimal Controllers for Nonlinear Systems

Gravity compensation and optimal control of actuated multibody system dynamics

Design an omnidirectional autonomous mobile robot based on non‐linear optimal control to track a specified path

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