Related papers: Characterising Robust Instances of Ultimate Positi…
This paper studies distributionally robust optimization (DRO) when the ambiguity set is given by moments for the distributions. The objective and constraints are given by polynomials in decision variables. We reformulate the DRO with…
Numerical stability is of great significance for discrete-time dynamic vehicle model. Among the unstable factors, low-speed singularity stands out as one of the most challenging issues, which arises from that the denominator of tire side…
This paper proposes a finitely terminating algorithm to solve reach-and-stay control problems for nonlinear systems. The algorithm is guaranteed to return a control strategy if the specification is robustly realizable. Such a feature is…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over continuous time. We analyse this problem with respect to the allowable control sets, which are assumed to be the image under a linear…
We are concerned with the nodal set of solutions to equations of the form \begin{equation*} -\Delta u = \lambda_+ \left(u^+\right)^{q-1} - \lambda_- \left(u^-\right)^{q-1} \quad \text{in $B_1$} \end{equation*} where $\lambda_+,\lambda_- >…
The robust disturbance rejection controller has been the subject of intensive research due to its undeniable importance for automation. Modern control theory tends to use model-based approaches versus model-free approaches, especially when…
The problem of linking the structure of a finite linear dynamical system with its dynamics is well understood when the phase space is a vector space over a finite field. The cycle structure of such a system can be described by the…
The existence and multiplicity of positive periodic solutions for second order non-autonomous singular dynamical systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. Our…
In this work, we show the consistency of an approach for solving robust optimization problems using sequences of sub-problems generated by ergodic measure preserving transformations. The main result of this paper is that the minimizers and…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
The existence and multiplicity of positive periodic solutions for first non-autonomous singular systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. The proof of our…
We consider the linear complementarity problem with uncertain data modeled by intervals, representing the range of possible values. Many properties of the linear complementarity problem (such as solvability, uniqueness, convexity, finite…
Empirical modelling often aims for the simplest model consistent with the data. A new technique is presented which quantifies the consistency of the model dynamics as a function of location in state space. As is well-known, traditional…
Robust control is a core approach for controlling systems with performance guarantees that are robust to modeling error, and is widely used in real-world systems. However, current robust control approaches can only handle small system…
We investigate in this work the validity of linear stochastic models for nonlinear dynamical systems. We exploit as our basic tool a previously proposed Rayleigh-Ritz approximation for the effective action of nonlinear dynamical systems…
Solutions to the interval observation problem for delayed impulsive and switched systems with $L_1$-performance are provided. The approach is based on first obtaining stability and $L_1/\ell_1$-to-$L_1/\ell_1$ performance analysis…
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…
Numerical software are widely used in safety-critical systems such as aircrafts, satellites, car engines and so on, facilitating dynamics control of such systems in real time, it is therefore absolutely necessary to verify their…
We study a class of ordinary differential equations with a non-Lipschitz point singularity, which admit non-unique solutions through this point. As a selection criterion, we introduce stochastic regularizations depending on the parameter…
It is well-known that when a positively expansive dynamical system is invertible then its underlying space is finite. C.Morales has introduced a decade ago a natural way to generalize positive expansiveness, by introducing other properties…