Polynomial static output feedback H ∞ control via homogeneous Lyapunov functions

Lin

2022

Aim at the fore and aft asymmetry of unmanned surface vehicle (USV) and the loss of linear velocity, a static output feedback (SOF) H ∞ control method is proposed by the sum of squares (SOS) based on two types of extended bounded real lemmas (EBRL) for heading regulation to guarantee the robustness and improve the rapidity. First, an asymmetric nonlinear heading error model with hydrodynamic parameters is established by the consideration of lack of linear velocity. Second, SOF controller with H ∞ performance is presented for the asymmetric nonlinear USV model, and it's SOS conditions to solve controller parameters is deduced from EBRL by homogeneous Lyapunov function (HERBL) to maintain the system robustness. Further, the solution of SOF H ∞ controller relies on the state feedback gain matrix, EBRL is deduced by quadratic Lyapunov function (QEBRL) to obtain the SOS conditions without the addition of an extended matrix to cut computing cost for the solution of the state feedback gain matrix.Finally, the heading control simulations for USV indicate that, QEBRL method takes less time for SOS conditions to solve the state feedback gain matrix, and SOF H ∞ system of HERBL has a superior performance on the transient response and the robustness. K E Y W O R D Sextended bounded real lemma (EBRL), heading regulation of USV, nonlinear heading error model, state feedback gain matrix, static output feedback (SOF) H ∞ control, sum of squares (SOS)

“…The heading error nonlinear model (10) is 4 dimensions and asymmetry. Two‐step SOS method is used to designed SOF

{H}_{\infty }

controller for (10), 13 and the SOS conditions for (10) is deduced from polynomial fuzzy system. On the solution procedure, the state feedback gain matrix is the premise of the solution of the SOF

{H}_{\infty }

controller.…”

Section: Heading Error State Control Modelmentioning

confidence: 99%

“…However, the iterative SOS process was cumbersome and complicated. Two‐step SOS has two steps to compute the parameters of SOF

{H}_{\infty }

Section: Introductionmentioning

confidence: 99%

Extended bounded real lemma based sum of squares for static output feedback H_∞ heading control

Lin

2022

“…Although their behavior can often be approximated by linear models which are easy to understand and to interpret. Unfortunately, some linear approximations are only valid for a given input range 11,12 . Hence, during the last decades there has been a tendency toward nonlinear modeling and identification in various application fields 13‐15 .…”

Section: Introductionmentioning

confidence: 99%

An efficient recursive identification algorithm for multilinear systems based on tensor decomposition

Wang

Yang

2021

There are many important fields involving the multilinear system identification. A great number of parameters to be identified is an important challenge, leading to the need for tensorial decomposition and modeling of such systems. This article is about the parameter estimation of the higher‐order multilinear systems with non‐Gaussian noises and to explore the role of tensor algebra in the multilinear model identification. A high‐dimension system identification problem is reformulated in terms of low‐dimension problems by using the tensorial decomposition technique. Further, applying the multi‐innovation identification theory, the recursive algorithm combining with the logarithmic p‐norms is investigated for multilinear systems with non‐Gaussian noises of low computational complexity. Finally, some simulation results illustrate the effectiveness of the proposed recursive identification method.

“…There have been many efforts and numerical methods in the literature on how to evaluate Lyapunov functions for several kinds of systems. Some of these methods are linear programming (LP), 3,4 linear matrix inequalities (LMI), [5][6][7] sum of squares (SOS), 8,9 artificial neural networks (ANN), 10,11 and genetic algorithms. 12,13 Polanski 3 first proposed an implementation of a Lyapunov function given by the infinity norm through LP.…”

Section: Introductionmentioning

confidence: 99%

“…By contrast, the methods based on SOS usually compute a polynomial Lyapunov function, as shown in the works. 8,9 But, methods based on SOS present conservatism and may fail in finding a Lyapunov function of a particular degree. As explained by Ahmadi and Parrilo, 9 this can be due to the gap between nonnegativity and SOS.…”

Section: Introductionmentioning

confidence: 99%

Learning‐based robust neuro‐control: A method to compute control Lyapunov functions

Rego

Araújo

2021

Nonlinear dynamical systems play a crucial role in control systems because, in practice, all the plants are nonlinear, and they are also a hopeful description of complex robot movements. To perform a control and stability analysis of a nonlinear system, usually, a Lyapunov function is used. In this article, we proposed a method to compute a control Lyapunov function (CLF) for nonlinear dynamics based on a learning robust neuro-control strategy. The procedure uses a deep neural network architecture to generate control functions supported by the Lyapunov stability theory. An estimation of the region of attraction is produced for advanced stability analysis. We implemented two numerical examples to compare the performance of the proposed technique with some existing methods.The proposed method computes a CLF that provides the stabilizability of the systems and produced better solutions to nonlinear systems in the design of stable controls without linear approximations and in the presence of disturbances.