| _version_ | 1866901252532600832 |
|---|---|
| author | mj, Rohith |
| author_facet | mj, Rohith |
| contents | <p>Classical viability theory studies whether a controlled dynamical system can be kept inside a prescribed constraint set over time. Given a state space <span><span>XX</span><span><span><span>X</span></span></span></span>, a control system <span><span>xt+1=f(xt,ut)x_{t+1}=f(x_t,u_t)</span><span><span><span><span>x</span><span><span><span><span><span><span><span>t</span><span>+</span>1</span></span></span><span></span></span></span></span></span><span>=</span></span><span><span>f</span><span>(</span><span><span>x</span><span><span><span><span><span><span>t</span></span></span><span></span></span></span></span></span><span>,</span><span><span>u</span><span><span><span><span><span><span>t</span></span></span><span></span></span></span></span></span><span>)</span></span></span></span>, and a safe set <span><span>K⊂XK\subset X</span><span><span><span>K</span><span>⊂</span></span><span><span>X</span></span></span></span>, the <strong>viability kernel</strong> is the set of initial states from which at least one admissible control strategy can keep the system inside <span><span>KK</span><span><span><span>K</span></span></span></span> for all future times.</p> <p>However, in real systems, two fundamental complications arise:</p> <ol> <li> <p><strong>Uncertainty</strong>: system evolution is stochastic rather than deterministic.</p> </li> <li> <p><strong>Partial observability</strong>: the controller does not directly observe the state.</p> </li> </ol> <p>Stochastic viability kernels generalize classical viability theory to this setting.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18343805 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | viability theory in stocastic control mj, Rohith viabity theory stocastic control <p>Classical viability theory studies whether a controlled dynamical system can be kept inside a prescribed constraint set over time. Given a state space <span><span>XX</span><span><span><span>X</span></span></span></span>, a control system <span><span>xt+1=f(xt,ut)x_{t+1}=f(x_t,u_t)</span><span><span><span><span>x</span><span><span><span><span><span><span><span>t</span><span>+</span>1</span></span></span><span></span></span></span></span></span><span>=</span></span><span><span>f</span><span>(</span><span><span>x</span><span><span><span><span><span><span>t</span></span></span><span></span></span></span></span></span><span>,</span><span><span>u</span><span><span><span><span><span><span>t</span></span></span><span></span></span></span></span></span><span>)</span></span></span></span>, and a safe set <span><span>K⊂XK\subset X</span><span><span><span>K</span><span>⊂</span></span><span><span>X</span></span></span></span>, the <strong>viability kernel</strong> is the set of initial states from which at least one admissible control strategy can keep the system inside <span><span>KK</span><span><span><span>K</span></span></span></span> for all future times.</p> <p>However, in real systems, two fundamental complications arise:</p> <ol> <li> <p><strong>Uncertainty</strong>: system evolution is stochastic rather than deterministic.</p> </li> <li> <p><strong>Partial observability</strong>: the controller does not directly observe the state.</p> </li> </ol> <p>Stochastic viability kernels generalize classical viability theory to this setting.</p> |
| title | viability theory in stocastic control |
| topic | viabity theory stocastic control |
| url | https://doi.org/10.5281/zenodo.18343805 |