36 problems

Equal-energy controllability conjecture. For any two flows with equal energies, the conclusion of Theorem 4 is true.

Let the control be restricted to the finite-dimensional subspace generated by Fourier modes indexed by … where $m$ is a mode index. Controllability conjecture. A control with this…

Let $(M,g)$ be a compact Riemannian manifold, and consider the wave maps equation from the circle to $M$. Two states are homotopic when they lie in the same homotopy class as maps…

Consider the diffusive Lotka–Volterra strongly competitive system on an interval $(0,L)$ with boundary-constrained controls, parameters $a>0$ and $b>1$ satisfying $b>a$, initial da…

Consider the diffusive Lotka–Volterra system with boundary controls and admissible states in $[0,1]\times[0,1]$, and let $(w_1^*,w_2^*)$ be an equilibrium lying strictly in the int…

Consider the laminated beam system with dynamic Venttsel-type boundary conditions and its linear operator defined in the paper. Boundary-control reduction conjecture. By applying C…

Brockett's smooth-dependence conjecture. There should be a solution for both the continuous-time Lyapunov equation and the right-invariant bilinear system that depends smoothly on…

The paper considers controllability results for diffeomorphism groups of simple polytopes, including generation of the identity component by exponentials of suitable vector fields…

Exact controllability criterion. The conditions in Theorem 1.2, namely

Let $(\mathcal{M},g)$ be a Riemannian manifold, and let $\phi:\mathbb{R}\times\mathbb{S}^1\to\mathcal{M}$ solve the controlled wave maps equation. For initial and final states…

Let $(\mathcal{M},g)$ be a general Riemannian manifold target for the controlled wave maps equation. The controllable space (or accessible space) is the set of target states reacha…

Consider the linear difference delay system with maximal delay parameter $\Lambda_N$, dimension $d$, and a single input, so that $m=1$. Assume that controllability holds and that t…

The paper studies boundary approximate controllability under positivity constraints for transport and heat systems. Applications conjecture. Other potential applications include mo…

Consider a semilinear reaction-diffusion system with state constraints, in a setting where the nonlinearity is globally Lipschitz but controlled trajectories may move away from tar…

Let $M$ be the quotient under consideration of a group of Heisenberg type, let $U\subset M$ be open, and let $T_{\rm GCC}(U)$ denote the geometric control time associated with $U$.…

Consider real-life dynamical systems modeled by differential equations and subject to intrinsic phenomena such as impulses, delays, memory, nonlocal conditions, and noise. Regard t…

Let a dynamical system be subject to perturbations involving delays, impulses, or memory. Controllability conjecture. Controllability of the system should not change under these pe…

Controllability-diameter conjecture. For every such Hamiltonian, the implication

Classical-to-quantum controllability conjecture. If the classical system is not small-time controllable, then the corresponding quantum system is not small-time controllable either…

One-switch controllability conjecture. If the smooth target is STLA at $\bar x$, then the target can be reached from every point in a neighborhood of $\bar x$ using a piecewise con…

Let $G$ be a connected simple graph, and let $A(G)$ denote its adjacency matrix. A graph is strongly uncontrollable using $A(G)$ if the pair $(A(G),b)$ is uncontrollable for every…

Let a two-control system be in the particular case where … Here $B_2$ denotes the second obstruction discussed in the paper, and $f_1$, $f_2$, and $R_1$ are the vector fields and b…

Let $\Omega$ be the rectangular domain described above, and let $L^2_{\operatorname{div}}(\Omega)$ denote the space of square-integrable divergence-free vector fields tangent to…

Controllability-invariance conjecture. Controllability of a system should not change under perturbations such as delays, impulses, or certain types of memory.

Indirect controllability conjecture. As in the constant-coefficient case, either the first line of or the condition $g_{21}\neq 0$ in $(a,b)\times\mathcal O$ is sufficient for indi…