Introduction to the Theory of Differential Inclusions

By G. Smirnov. 2002

597 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/d74013a77a17fbb215b3dacb249b0ee2aecd536f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Frank L. Lewis
2. Kyriakos G. Vamvoudakis
3. Derong Liu
4. Jason D. Lee
5. Hamidreza Modares
6. Warren E. Dixon
7. Shubhendu Bhasin
8. Marcus Johnson

In Control and Systems Engineering

1. Frank L. Lewis
2. Kyriakos G. Vamvoudakis
3. Derong Liu
4. Warren E. Dixon
5. Shubhendu Bhasin
6. Marcus Johnson
7. Rushikesh Kamalapurkar
8. Jong-Shi Pang

Citations in the corpus

• Optimal control of the sweeping process over polyhedral controlled sets (2015, unknown): “, [25,40,44] and the references therein.”
• Saturated control design for linear differential inclusions subject to disturbance (2009, background): “The reason is that the system described by an LDI can possess strong nonlinearity and time-varying uncertainty [1, 2].”
• A Comparison between Two Theories for Multi-Valued Semiflows and Their Asymptotic Behaviour (2003, unknown): “[This anomaly can be corrected by redefining F(1) to be {0, 1}, or the whole interval [0, 1], see Smirnov [29].”
• A novel actor-critic-identifier architecture for approximate optimal control of uncertain nonlinear systems (2013, background): “Using Filippov’s theory of differential inclusions (Filippov, 1964; Smirnov, 2002), the existence of solutions can be established for ẏ ∈ K [h](y, t), where K [h] ,  δ>0  μM=0 coh(B(y, δ) − M, t), where  μM=0 denotes the intersection over all sets M of Lebesgue measure zero, co denotes convex clo”
• Stochastic Subgradient Method Converges on Tame Functions (2018, methodology): “Throughout, we will mostly use standard notation on differential inclusions, as set out for example in the monographs of Borkar [5], Clarke-Ledyaev-Stern-Wolenski [10], and Smirnov [32].”
• Differential variational inequalities (2008, background): “Namely, the existing DI theory as documented in such references as [10,32,66,89] is cast in a very abstract framework.”
• Impulsive differential equations and inclusions (2006, unknown): “For a thumbnail sketch of the literature on differential inclusions, we suggest [22, 96, 97, 104, 106– 111, 118, 121, 146, 179, 198, 211, 213, 215, 221].”
• Sampling best response dynamics and deterministic equilibrium selection (2015, background): “For further background, see Aubin and Cellina (1984), Smirnov (2002), and Benaı̈m et al. (2005, henceforth BHS).”