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This paper revisits a classical challenge in the design of stabilizing controllers for nonlinear systems with a norm-bounded input constraint. By extending Lin-Sontag's universal formula and introducing a generic (state-dependent) scaling…
Safe stabilization is a significant challenge for quadrotors, which involves reaching a goal position while avoiding obstacles. Most of the existing solutions for this problem rely on optimization-based methods, demanding substantial…
In this paper we introduce the concept of universal stabilizability: the condition that every solution of a nonlinear system can be globally stabilized. We give sufficient conditions in terms of the existence of a control contraction…
Given a Control Lyapunov Function (CLF), Sontag's famous Formula provides a nonlinear state-feedback guaranteeing asymptotic stability of the setpoint. At the same time, a cost function that depends on the CLF is minimized. While there…
In this paper input-to-state practically stabilizing control laws for retarded, control-affine, nonlinear systems with actuator disturbance are investigated. The developed methodology is based on the Arstein's theory of control Liapunov…
A common tool in system theory for formulating control laws that achieve local asymptotic stability are Control Lyapunov functions (CLFs), while Control Barrier functions (CBFs) are typically employed to enforce safety constraints.…
A combination of control Lyapunov functions (CLFs) and control barrier functions (CBFs) forms an efficient framework for addressing control challenges in safe stabilization. In our previous research, we developed an analytical control…
In this paper, we address the problem of synthesizing safe and stabilizing controllers for nonlinear systems subject to complex safety specifications and input constraints. We introduce the Universal Barrier Function (UBF), a single…
We propose the first generalization of Sontag s universal controller to systems not affine in the control, particularly, to PDEs with boundary actuation. We assume that the system admits a control Lyapunov function (CLF) whose derivative,…
To bring complex systems into real world environments in a safe manner, they will have to be robust to uncertainties - both in the environment and the system. This paper investigates the safety of control systems under input disturbances,…
An interlaced method to learn and control nonlinear system dynamics from a set of demonstrations is proposed, under a constrained optimization framework for the unsupervised learning process. The nonlinear system is modelled as a mixture of…
This paper investigates the safety analysis and verification of nonlinear systems subject to high-relative-degree constraints and unknown disturbance. The closed-form solution of the high-order control barrier functions (HOCBF) optimization…
We present a novel technique for solving the problem of safe control for a general class of nonlinear, control-affine systems subject to parametric model uncertainty. Invoking Lyapunov analysis and the notion of fixed-time stability (FxTS),…
We develop an optimization-free framework for safe stabilization of single-input control-affine nonlinear systems with a given control Lyapunov function (CLF) and a given control barrier function (CBF), where the desired equilibrium lies in…
Barrier functions (also called certificates) have been an important tool for the verification of hybrid systems, and have also played important roles in optimization and multi-objective control. The extension of a barrier function to a…
Safe control with guarantees generally requires the system model to be known. It is far more challenging to handle systems with uncertain parameters. In this paper, we propose a generic algorithm that can synthesize and verify safe…
In this paper the existence of a quadratic control Lyapunov function for bilinear systems is considered. The existence of a control Lyapunov function ensures the existence of a control law which ensures the global asymptotic stability of…
This paper studies control synthesis for a general class of nonlinear, control-affine dynamical systems under additive disturbances and state-estimation errors. We enforce forward invariance of static and dynamic safe sets and convergence…
This paper presents a constraint-lifting control framework for designing stabilizing controllers that guarantee the forward invariance of a prescribed safe set. State-of-the-art safety-enforcing methods, such as control barrier functions…
We present verifiable conditions for synthesizing a single smooth Lyapunov function that certifies both asymptotic stability and safety under bounded controls. These sufficient conditions ensure the strict compatibility of a control barrier…