Constraints in nonlinear L2-stable networked control

The paper derives a robust networked controller design method for systems with saturation where the delay is large and unknown, as in unidirectional flow-control. A classical linear robust criterion is first formulated in terms of the sensitivityand complementary sensitivity functions. Based on the Popov-criterion a new asymptotic constraint is derived, which specifies the minimum amount of low frequency gain in the sensitivity function, to guarantee non-linear closed loop L2-stability. This result guides the selection of the design criterion, thereby adjusting the linear controller design for better handling of delay and saturation. The controller design method then uses gridding to pre-compute the L2 stability region. Based on the precomputed stability region, a robust L2-stable controller can be selected. Alternatively, an adaptive controller could recompute L2-stable controllers on-line using the pre-computed stability region. Simulations show that the controller meets the specified stability and performance requirements.

[1]  R. Evans,et al.  Stabilization with data-rate-limited feedback: tightest attainable bounds , 2000 .

[2]  Graham C. Goodwin,et al.  Architectures and coder design for networked control systems , 2008, Autom..

[3]  Thomas G. Bifano,et al.  Development of a MEMS microvalve array for fluid flow control , 1998 .

[4]  Bruce A. Francis,et al.  Feedback Control Theory , 1992 .

[5]  Graham C. Goodwin,et al.  An MPC-based nonlinear quantizer for bit rate constrained networked control problems with application to inner loop power control in WCDMA , 2011, 2011 9th IEEE International Conference on Control and Automation (ICCA).

[6]  Theodore S. Rappaport,et al.  Millimeter Wave Wireless Communications , 2014 .

[7]  J. Baillieul.  Feedback coding for information-based control: operating near the data-rate limit , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[8]  Ulf Jönsson,et al.  Optimization of integral quadratic constraints , 1999 .

[9]  I. Sandberg.  A frequency-domain condition for the stability of feedback systems containing a single time-varying nonlinear element , 1964 .

[10]  Graham C. Goodwin,et al.  Optimal controller design for networked control systems , 2008 .

[11]  S. Gutman,et al.  Quantitative measures of robustness for systems including delayed perturbations , 1989 .

[12]  C. A. Desoer,et al.  Nonlinear Systems Analysis , 1978 .

[13]  Graham C. Goodwin,et al.  Adaptive filtering prediction and control , 1984 .

[14]  George M. Siouris,et al.  Applied Optimal Control: Optimization, Estimation, and Control , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[15]  Daniel E. Quevedo,et al.  Design of embedded filters for inner-loop power control in wireless CDMA communication systems , 2012 .

[16]  M. Vajta.  Some remarks on Padé-approximations , 2000 .

[17]  Lei Ying,et al.  Communication Networks - An Optimization, Control, and Stochastic Networks Perspective , 2014 .

[18]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[19]  Graham C. Goodwin,et al.  Constrained Control and Estimation: an Optimization Approach , 2004, IEEE Transactions on Automatic Control.

[20]  Bore-Kuen Lee,et al.  Power control of cellular radio systems via robust Smith prediction filter , 2004 .

[21]  Karl Johan Åström,et al.  Adaptive Control , 1989, Embedded Digital Control with Microcontrollers.

[22]  G. Zames.  On the input-output stability of time-varying nonlinear feedback systems Part one: Conditions derived using concepts of loop gain, conicity, and positivity , 1966 .

[23]  Torsten Söderström,et al.  LQG-optimal feedforward regulators , 1988, Autom..

[24]  Yuanqing Xia,et al.  Design and Stability Criteria of Networked Predictive Control Systems With Random Network Delay in the Feedback Channel , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[25]  Petros A. Ioannou,et al.  Traffic flow modeling and control using artificial neural networks , 1996 .

[26]  Graham C. Goodwin,et al.  Analysis and design of networked control systems using the additive noise model methodology , 2010 .

[27]  Graham C. Goodwin,et al.  A moving horizon approach to Networked Control system design , 2004, IEEE Transactions on Automatic Control.

[28]  Mrdjan Jankovic,et al.  Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems , 2001, IEEE Trans. Autom. Control..