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Volume 8 Issue 1
Jan.  2021

IEEE/CAA Journal of Automatica Sinica

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Mehdi Firouznia and Qing Hui, "On Performance Gauge of Average Multi-Cue Multi-Choice Decision Making: A Converse Lyapunov Approach," IEEE/CAA J. Autom. Sinica, vol. 8, no. 1, pp. 136-147, Jan. 2021. doi: 10.1109/JAS.2020.1003471
Citation: Mehdi Firouznia and Qing Hui, "On Performance Gauge of Average Multi-Cue Multi-Choice Decision Making: A Converse Lyapunov Approach," IEEE/CAA J. Autom. Sinica, vol. 8, no. 1, pp. 136-147, Jan. 2021. doi: 10.1109/JAS.2020.1003471

On Performance Gauge of Average Multi-Cue Multi-Choice Decision Making: A Converse Lyapunov Approach

doi: 10.1109/JAS.2020.1003471
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  • Motivated by the converse Lyapunov technique for investigating converse results of semistable switched systems in control theory, this paper utilizes a constructive induction method to identify a cost function for performance gauge of an average, multi-cue multi-choice (MCMC), cognitive decision making model over a switching time interval. It shows that such a constructive cost function can be evaluated through an abstract energy called Lyapunov function at initial conditions. Hence, the performance gauge problem for the average MCMC model becomes the issue of finding such a Lyapunov function, leading to a possible way for designing corresponding computational algorithms via iterative methods such as adaptive dynamic programming. In order to reach this goal, a series of technical results are presented for the construction of such a Lyapunov function and its mathematical properties are discussed in details. Finally, a major result of guaranteeing the existence of such a Lyapunov function is rigorously proved.

     

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  • [1]
    D. Nunes, J. Sa Silva, and F. Boavida, A Practical Introduction to Human-in-the-Loop Cyber-Physical Systems. Wiley-IEEE Press, 2018.
    [2]
    P. L. Smith and R. Ratcliff, “Psychology and neurobiology of simple decisions,” Trends in Neurosciences, vol. 27, no. 3, pp. 161–168, 2004. doi: 10.1016/j.tins.2004.01.006
    [3]
    R. Bogacz, E. Brown, J. Moehlis, P. Holmes, and J. D. Cohen, “The physics of optimal decision making: A formal analysis of models of performance in two-alternative forced-choice tasks,” Psychological Review, vol. 113, no. 4, pp. 700–765, 2006. doi: 10.1037/0033-295X.113.4.700
    [4]
    G. Deco, E. T. Rolls, L. Albantakis, and R. Romo, “Brain mechanisms for perceptual and reward-related decision-making,” Progress in Neurobiology, vol. 103, pp. 194–213, 2013. doi: 10.1016/j.pneurobio.2012.01.010
    [5]
    T. L. Lai, “Asymptotic optimality of invariant sequential probability ratio tests,” The Annals of Statistics, pp. 318–333, 1981.
    [6]
    D. van Ravenzwaaij, H. L. van der Maas, and E.-J. Wagenmakers, “Optimal decision making in neural inhibition models.,” Psychological Review, vol. 119, no. 1, pp. 201, 2012. doi: 10.1037/a0026275
    [7]
    P. Holmes and J. D. Cohen, “Optimality and some of its discontents: Successes and shortcomings of existing models for binary decisions,” Topics in Cognitive Science, vol. 6, no. 2, pp. 258–278, 2014. doi: 10.1111/tops.12084
    [8]
    A. Diederich and P. Oswald, “Sequential sampling model for multiattribute choice alternatives with random attention time and processing order, ” Frontiers in Human Neuroscience, vol. 8, Article no. 697, 2014.
    [9]
    M. Usher and J. L. McClelland, “The time course of perceptual choice: The leaky, competing accumulator model,” Psychological Review, vol. 108, no. 3, pp. 550–592, 2001. doi: 10.1037/0033-295X.108.3.550
    [10]
    M. Firouznia, C. Peng, and Q. Hui, “Toward building a humancognition-in-the-loop supervisory control system for humanized decision-making, ” in Proc. 13th Annu. IEEE Int. Systems Conf., Orlando, FL, April 2019.
    [11]
    M. Firouznia, “Human-cognition-in-the-loop: A framework to include decision process in closed loop control,” Ph.D. dissertation, Department of Electrical and Computer Engineering, University of NebraskaLincoln, Lincoln, NE, 2019.
    [12]
    Q. Hui, W. M. Haddad, J. M. Bailey, and T. Hayakawa, “A stochastic mean field model for an excitatory and inhibitory synaptic drive cortical neuronal network,” IEEE Trans. Neural Netw. Learn. Syst., vol. 25, no. 4, pp. 751–763, 2014. doi: 10.1109/TNNLS.2013.2281065
    [13]
    C. Altafini, “Consensus problems on networks with antagonistic interactions,” IEEE Trans. Automat. Control, vol. 58, no. 4, pp. 935–946, 2013. doi: 10.1109/TAC.2012.2224251
    [14]
    Y. Zhang and Y. Liu, “Nonlinear second-order multi-agent systems subject to antagonistic interactions without velocity constraints,” Applied Math. Comput., vol. 364, no. 1, 2020.
    [15]
    D. S. Bernstein, Matrix Mathematics, 2nd ed. Princeton, NJ: Princeton Univ. Press, 2009.
    [16]
    D. Vickers, “Evidence for an accumulator model of psychophysical discrimination,” Ergonomics, vol. 13, no. 1, pp. 37–58, 1970. doi: 10.1080/00140137008931117
    [17]
    S. Lang, Differential and Riemannian Manifolds. New York, NY: Springer, 1995.
    [18]
    L. Vu and D. Liberzon, “Common Lyapunov functions for families of commuting nonlinear systems,” Syst. Control Lett., vol. 54, pp. 405–416, 2005. doi: 10.1016/j.sysconle.2004.09.006
    [19]
    Q. Hui, “Semistability and robustness analysis for switched systems,” Eur. J. Control, vol. 17, pp. 73–88, 2011. doi: 10.3166/ejc.17.73-88
    [20]
    K. S. Narendra and J. Balakrishnan, “A common Lyapunov function for stable LTI systems with commuting A-matrices,” IEEE Trans. Automat. Control, vol. 39, no. 12, pp. 2469–2471, 1994. doi: 10.1109/9.362846
    [21]
    W. M. haddad, V. Chellaboina, and Q. Hui, Nonnegative and Compartmental Dynamical Systems. Princeton, NJ: Princeton Univ. Press, 2010.
    [22]
    W. M. Haddad and V. Chellaboina, Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach. Princeton, NJ: Princeton Univ. Press, 2008.
    [23]
    H. A. Simon, “Invariants of human behavior,” Annual Review of Psychology, vol. 41, pp. 1–20, 1990. doi: 10.1146/annurev.ps.41.020190.000245
    [24]
    Q. Hui, W. M. Haddad, and S. P. Bhat, “Finite-time semistability and consensus for nonlinear dynamical networks,” IEEE Trans. Automat. Control, vol. 53, no. 8, pp. 1887–1900, 2008. doi: 10.1109/TAC.2008.929392
    [25]
    M. S. Branicky, “Multiple Lyapunov functions and other analysis tools for switched and hybrid systems,” IEEE Trans. Automat. Control, vol. 43, no. 4, pp. 475–482, 1998. doi: 10.1109/9.664150
    [26]
    E. Sontag and Y. Lin, “Stabilization with respect to noncompact sets: Lyapunov characterizations and effect of bounded inputs, ” in Proc. IFAC Symp. Nonlinear Control Systems Design 1992–Bordeaux, France, ser. IFAC Symposia Series, no. 7. Pergamon Press, 1993, pp. 43–49.
    [27]
    Q. Hui and W. M. Haddad, “Semistability of switched dynamical systems. Part I: Linear system theory,” Nonlinear Anal. Hybrid Syst., vol. 3, pp. 343–353, 2009. doi: 10.1016/j.nahs.2009.02.003
    [28]
    Y. Yang, D. Wunsch, and Y. Yin, “Hamiltonian-driven adaptive dynamic programming for continuous nonlinear dynamical systems,” IEEE Trans. Neural Netw. Learn. Syst., vol. 28, no. 8, pp. 1929–1940, 2017. doi: 10.1109/TNNLS.2017.2654324
    [29]
    K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control. Upper Saddle River, NJ: Prentice Hall, 1996.
    [30]
    L. Vandenberghe and S. Boyd, “Semidefinite programming,” SIAM Rev., vol. 138, pp. 49–95, 1996.
    [31]
    R. T. Rockafellar, Convex Analysis. Princeton, NJ: Princeton Univ. Press, 1979.
    [32]
    J. Kurzweil, “On the inversion of Lyapunov’s second theorem on stability of motion, ” Amer. Math. Soc. Transl., vol. 24, pp. 19–77, 1963, translated from Czechoslovak Math. J., vol. 81, pp. 217–259; 455–484, 1956.
    [33]
    F. W. Wilson, “Smoothing derivatives of functions and applications,” Trans. Amer. Math. Soc., vol. 139, pp. 413–428, 1969. doi: 10.1090/S0002-9947-1969-0251747-9
    [34]
    W. P. Dayawansa and C. F. Martin, “A converse Lyapunov theorem for a class of dynamical systems which undergo switching,” IEEE Trans. Automat. Control, vol. 44, no. 4, pp. 751–760, 1999. doi: 10.1109/9.754812

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    Highlights

    • Used a novel constructive method to prove the existence of a cost function that can put the dynamic behavior of multi-cue multi-choice decision making into an optimum perspective.
    • Used a Lyapunov-based control-theoretic approach to study dynamic properties decision making models.
    • Discovered a new converse Lyapunov theorem for a class of switched linear systems.

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