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Two-wheeled inverted pendulum robots are designed for self-balancing and they have remarkable advantages. In this paper, a new configuration and consequently dynamic model of one specific robot is presented and its dynamic behavior is…
A novel method for control of dynamical systems, proposed in the paper, ensures an output signal belonging to the given set at any time. The method is based on a special change of coordinates such that the initial problem with given…
This article establishes the foundation for a new theory of invariant/integral manifolds for non-autonomous dynamical systems. Current rigorous support for dimensional reduction modelling of slow-fast systems is limited by the rare events…
We tackle the boundary control and estimation problems for a class of viscous Hamilton-Jacobi PDEs, considering bilateral actuation and sensing, i.e., at the two boundaries of a 1-D spatial domain. First, we solve the nonlinear trajectory…
A time optimal attitude control problem is studied for the dynamics of a rigid body. The objective is to minimize the time to rotate the rigid body to a desired attitude and angular velocity while subject to constraints on the control…
This paper addresses the closed-loop control of an actuator with both a continuous input variable (motor torque) and a discrete input variable (mode selection). In many applications, robots have to bear large loads while moving slowly and…
We present a hierarchical whole-body controller leveraging the full rigid body dynamics of the wheeled bipedal robot Ascento. We derive closed-form expressions for the dynamics of its kinematic loops in a way that readily generalizes to…
This paper presents a new geometric adaptive control system with state inequality constraints for the attitude dynamics of a rigid body. The control system is designed such that the desired attitude is asymptotically stabilized, while the…
In this paper, we study linear control systems with positive bounded orbits. We show that the existence of positive bounded orbits imposes strong algebraic and topological constraints on the state space. In fact, a linear control system has…
The normal and the inverted pendulum continue to be one of the main physical models and metaphors in science. The inverted pendulum is also a classic study case in control theory. In this paper we consider a special demonstration version of…
Adaptive control approaches yield high-performance controllers when a precise system model or suitable parametrizations of the controller are available. Existing data-driven approaches for adaptive control mostly augment standard…
Positive systems naturally arise in situations where the model tracks physical quantities. Although the linear case is well understood, analysis and controller design for nonlinear positive systems remain challenging. Model reduction…
Optimal nonlinear damping control was recently introduced for the second-order SISO systems, showing some advantages over a classical PD feedback controller. This paper summarizes the main theoretical developments and properties of the…
In order for a humanoid robot to perform loco-manipulation such as moving an object while walking, it is necessary to account for sustained or alternating external forces other than ground-feet reaction, resulting from humanoid-object…
Using extensive particle-based simulations, we investigate out-of-equilibrium pattern dynamics in an oppositely driven binary particle system in two dimensions. A surprisingly rich dynamical behavior including lane formation, jamming,…
The canonical proportional-integral-derivative (PID) control approach has been widely used in industrial application due to their simplicity and ease of use. However, its corresponding controller parameters are hard to be adjusted,…
For a wide class of second order nonlinear non-autonomous models, we illustrate that combining proportional state control with the feedback that is proportional to the derivative of the chaotic signal, allows to stabilize unstable motions…
We consider a quasi-variational inequality governed by a moving set. We employ the assumption that the movement of the set has a small Lipschitz constant. Under this requirement, we show that the quasi-variational inequality has a unique…
We consider the optimal control problem of stochastic evolution equations in a Hilbert space under a recursive utility, which is described as the solution of a backward stochastic differential equation (BSDE). A very general maximum…
One of the most important branches of nonlinear control theory is the so-called sliding-mode. Its aim is the design of a (nonlinear) feedback law that brings and maintains the state trajectory of a dynamic system on a given sliding surface.…