Towards Analog Memristive Controllers

Memristors, initially introduced in the 1970s, have received increased attention upon successful synthesis in 2008. Considerable work has been done on modeling and applications in specific areas, however, very little is known on the potential of memristors for control applications. Being nanoscopic variable resistors, it is intuitive to think of using them as a variable gain. The main contribution of this paper is the development of a memristive analog gain control framework and theoretic foundation of a control strategy which can be implemented using this framework. Analog memristive controllers may find applications in control of large array of miniaturized devices where robust and adaptive control is needed due to parameter uncertainty and ageing issues.

[1]  H. Fujioka,et al.  Bounds for the BMI Eigenvalue Problem:A Good Lower Bound and A Cheap Upper Bound , 1997 .

[2]  Victor Solo,et al.  On the stability of slowly time-varying linear systems , 1994, Math. Control. Signals Syst..

[3]  J. Gorman,et al.  Feedback Control of MEMS to Atoms , 2012 .

[4]  Massimiliano Di Ventra,et al.  Memristive model of amoeba learning. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Kyungmin Kim,et al.  Memristor Applications for Programmable Analog ICs , 2011, IEEE Transactions on Nanotechnology.

[6]  Fernando Corinto,et al.  A Boundary Condition-Based Approach to the Modeling of Memristor Nanostructures , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[7]  David P. Dobkin,et al.  The quickhull algorithm for convex hulls , 1996, TOMS.

[8]  M. Kawanishi,et al.  BMI Global Optimization using Parallel Branch and Bound Method with a Novel Branching Method , 2007, 2007 American Control Conference.

[9]  Peng Li,et al.  Dynamical Properties and Design Analysis for Nonvolatile Memristor Memories , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[10]  William D. Jemison,et al.  Variable gain amplifier circuit using titanium dioxide memristors , 2011, IET Circuits Devices Syst..

[11]  Massimiliano Di Ventra,et al.  Experimental demonstration of associative memory with memristive neural networks , 2009, Neural Networks.

[12]  Itzhak Barkana,et al.  Simple adaptive control – a stable direct model reference adaptive control methodology – brief survey , 2014 .

[13]  Paul E. Hasler,et al.  Tunable Highly Linear Floating-Gate CMOS Resistor Using Common-Mode Linearization Technique , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[14]  Dimitri Jeltsema,et al.  Port-Hamiltonian Formulation of Systems With Memory , 2012, Proceedings of the IEEE.

[15]  Masakazu Kojima,et al.  Branch-and-Cut Algorithms for the Bilinear Matrix Inequality Eigenvalue Problem , 2001, Comput. Optim. Appl..

[16]  Uri C. Weiser,et al.  TEAM: ThrEshold Adaptive Memristor Model , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[17]  Stephen J. Wolf,et al.  The elusive memristor: properties of basic electrical circuits , 2008, 0807.3994.

[18]  Arkadi Nemirovski,et al.  Lectures on modern convex optimization - analysis, algorithms, and engineering applications , 2001, MPS-SIAM series on optimization.

[19]  James Lam,et al.  Static Output Feedback Stabilization: An ILMI Approach , 1998, Autom..

[20]  D. Stewart,et al.  The missing memristor found , 2008, Nature.

[21]  E. Yaz Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[22]  Jun Wang,et al.  Global uniform asymptotic stability of memristor-based recurrent neural networks with time delays , 2010, The 2010 International Joint Conference on Neural Networks (IJCNN).

[23]  Dimitri Jeltsema,et al.  Memristive port-Hamiltonian Systems , 2010 .

[24]  H. H. Rosenbrook The Stability of Linear Time-dependent Control Systems† , 1963 .

[25]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[26]  E. Kreyszig Introductory Functional Analysis With Applications , 1978 .

[27]  G. Papavassilopoulos,et al.  A global optimization approach for the BMI problem , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[28]  A. Delgado The memristor as controller , 2010, 2010 IEEE Nanotechnology Materials and Devices Conference.

[29]  Katsuhiko Ogata,et al.  Modern Control Engineering , 1970 .

[30]  Stephen P. Boyd,et al.  A path-following method for solving BMI problems in control , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[31]  Stephen P. Boyd,et al.  Low-authority controller design via convex optimization , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[32]  Wei Yang Lu,et al.  Nanoscale memristor device as synapse in neuromorphic systems. , 2010, Nano letters.

[33]  L. Chua Memristor-The missing circuit element , 1971 .

[34]  Y. Pershin,et al.  Second and higher harmonics generation with memristive systems , 2012, 1202.4727.

[35]  D. Owens,et al.  Sufficient conditions for stability of linear time-varying systems , 1987 .

[36]  Faruk Kazi,et al.  Energy and power based perspective of memristive controllers , 2013, 52nd IEEE Conference on Decision and Control.

[37]  Jacquelien M. A. Scherpen,et al.  Memristive port-Hamiltonian control: Path-dependent damping injection in control of mechanical systems , 2013, Eur. J. Control.

[38]  Massimiliano Di Ventra,et al.  Practical Approach to Programmable Analog Circuits With Memristors , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[39]  L.O. Chua,et al.  Memristive devices and systems , 1976, Proceedings of the IEEE.

[40]  Hyunsang Hwang,et al.  Neuromorphic Character Recognition System With Two PCMO Memristors as a Synapse , 2014, IEEE Transactions on Industrial Electronics.