Gradient Update Law Research Articles

Shape Servoing of Deformable Objects using Adaptive Deformation Model Estimation

In this paper, we propose an adaptive shape servoing method to deform a soft object into a desired 3-D shape. The high dimensional representation and the unknown deformation properties of the soft object pose a challenge to actively manipulate its shape. To address this issue, we develop a method to compute the deformation Jacobian matrix in real-time. The Jacobian is estimated using a set of basis functions and its corresponding parameters to capture the dynamics of the system and relate the applied input motion to changes in the soft object's shape. An integral concurrent learning (ICL) based adaptive update law is derived using Lyapunov analysis to estimate the deformation parameters and prove its convergence. A physics-based simulation is used to validate the proposed method and controller by performing manipulation tasks with different desired configurations. The performance is compared with a standard gradient update law to demonstrate the accuracy and robustness of our approach.

A composite adaptive tracking controller for dynamically positioned surface vessels with only position measurements

This work presents an alternative solution to the tracking control of dynamically positioned surface vessels having uncertainties associated with their dynamical model while using only vessel’s position measurements. Specifically, a surrogate state filter in conjunction with a composite parameter estimation algorithm is applied to ensure semi-global asymptotic convergence of the states of the vessel to their respective desired values. As opposed to its solely gradient based counterparts, the proposed algorithm utilizes an update law that is composed of a gradient update law driven by position tracking error and a least squares update law driven by the prediction error. This enables the proposed controller to compensate for the model uncertainties in a relatively shorter period of time. Rigorous analysis based on Lyapunov type approaches are applied in order to ensure the stability and boundedness of the closed loop system. Comparative simulations performed on the model of a surface vessel are presented in order to illustrate the tracking, and parameter estimation performance of the proposed controller/adaptation algorithm.

Decentralized adaptive consensus control for discrete‐time heterogeneous semiparametric multiagent systems

SummaryDifferent from the consensus control of traditional multiagent systems, this paper studies the decentralized adaptive consensus control for discrete‐time heterogeneous hidden leader‐following semiparametric multiagent system, in which the dynamic equation of each agent has both parametric uncertainties and nonparametric uncertainties. In the considered system, there is a hidden leader agent who can receive the reference signal, but it can only affect the states of those agents who are in its neighborhood. For other following agents, they do not know the leader's existence or the reference signal, and they can only receive information from their neighbors. Our goal is to design decentralized adaptive controllers to make sure that all agents can track the reference signal, and the closed‐loop system achieves consensus in the presence of mutual coupling relations. Due to the existence of both parametric and nonparametric uncertainties in the system, we need to estimate them separately. For the parametric part, we propose a novel dead zone with threshold converging to zero to modify the traditional gradient update law, while for the nonparametric part, we introduce an auxiliary variable including both two uncertainties to facilitate the nonparametric uncertainties compensation. Based on the certainty equivalence principle in adaptive control theory, the decentralized adaptive controller is designed for each agent to make sure that all of them can track the reference signal. Finally, under the proposed control protocol, strict mathematical proofs are given by using Lyapunov theory; then, simulation results are provided to demonstrate the effectiveness of proposed decentralized adaptive controllers.

A model-based algorithm for maximum power point tracking of PV systems using exact analytical solution of single-diode equivalent model

A novel model-based technique is presented for maximum power point tracking (MPPT) of photovoltaic (PV) systems. In this paper, an exact single-diode circuit model without any simplification or approximation is considered. Using datasheet information, an adaptive identification technique is utilized to find the electrical parameters uniquely and precisely. After this offline identification scheme, an estimation of solar irradiation is achieved from real-time measurements of PV voltage and current. In the next step, the gradient function of power with respect to voltage is represented from strongly concave mapping between power and voltage. Since the nonlinear gradient consists the complex Lambert W-function, a mathematical formulation is derived to approximate it with conventional logarithmic functions. Finally, a gradient update law is derived to find the unknown optimal voltage value, which results in maximum power generation for any environmental condition. The proposed approach guarantees exponential convergence with highly accurate steady-state performance.

Modular design of adaptive robust controller for strict-feedback stochastic nonlinear systems

A modular approach of the estimation-based design in adaptive linear control systems has been extended to the adaptive robust control of strict-feedback stochastic nonlinear systems with additive standard Wiener noises and constant unknown parameters. By using Ito’s differentiation rule, nonlinear damping and adaptive Backstepping procedure, the input-to-state stable controller of global stabilization in probability is developed, which guarantees that system states are bounded and the system has a robust stabilization. According to Swapping technique, we develop two filters and convert dynamic parametric models into static ones to which the gradient update law is designed. Transient performance of the system is estimated by the norm of error. Results of simulation show the effectiveness of the control algorithms. The modular design, which has a concise hierarchy, is more flexible and versatile than a Lyapunov-based algorithm.

Adaptive Tracking and Regulation of a Wheeled Mobile Robot With Controller/Update Law Modularity

A new adaptive controller is developed for wheeled mobile robots with parametric uncertainty in the dynamic model. The main theoretical contribution is the modular manner in which the control law and parameter update law are designed. This feature allows for design flexibility in the selection of the update law, and can be exploited to improve the transient response of the adaptive controller. The proposed controller also has the important feature of being applicable to both the tracking and regulation problems. The modularity of the adaptive controller is experimentally demonstrated on a K2A Cybermotion mobile robot that has been modified to allow for the implementation of torque-level control inputs. In particular, the adaptive controller with a gradient update law is evaluated vis-a/spl grave/-vis a least-squares update law.

A composite adaptive output feedback tracking controller for robotic manipulators

This paper provides a solution to the composite adaptive output feedback tracking control problem for robotic manipulators. The proposed controller utilizes an update law that is a composite of a gradient update law driven by the link position tracking error and a least squares update law driven by the prediction error. In order to remove the controller's dependence on link velocity measurements, a linear filter and a new prediction error formulation are designed. The controller provides semi-global asymptotic link position tracking performance. Experimental results illustrate that the proposed controller provides improved link position tracking error transient performance and faster parameter estimate convergence in comparsion to the same controller using a gradient update law.

Robust continuous-time adaptive control by parameter projection

One considers the problem of adaptive control of a continuous-time plant of arbitrary relative degree, in the presence of bounded disturbances as well as unmodeled dynamics. The adaptation law one considers is the usual gradient update law with parameter projection, the latter being the only robustness enhancement modification employed. One shows that if the unmodeled dynamics, which consists of multiplicative as well as additive system uncertainty, is small enough, then all the signals in the closed-loop system are bounded

Conditions for preservation of stability of adaptive controllers for systems with unmodeled delay

Some recent results from the mathematical literature are used to derive conditions under which stability of an adaptive controlled system (first-order plant with output feedback) is preserved in spite of the presence of a time delay in the plant input. Bounds on the delay, for which stability is preserved, are derived for three robust versions of the gradient update law: fixed sigma modification with and without normalization and a time-varying sigma modification. >