Abstract
It is a common experience that celebrations constitute a break in the usual commitments of daily life, during which the mind is led to indulge over the developments of the past. This especially applies to me now, at the beginning of these few lines written for the 65th birthday of Professor Antonio Ruberti. In the far 1970, when I was working at the laurea thesis in Electrical Engineering at the Politecnico di Milano, the name of Professor Ruberti was already associated with the forward line of research activity in systems and control, an area I discovered thanks to the classes given at the Politecnico by Professor Emanuele Biondi and Professor Guido Guardabassi. To my young mind of those days, automaticaworld appeared as a spring of genuine science in a paraphernalia of engineering techniques. The thesis subject was evolving around the stability and structural properties of linear systems with periodically varying coefficients. This was my first contact with the realm of PSICO (Periodic Sistems Identification, Control and Optimization), a contact which had to prolong in the decades to come.
A stroll in literature on periodic systems identification, control and optimization over more than 20 years
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References
Structural properties and canonical decomposition
Bittanti S., Deterministic and stochastic linear periodic systems,in Time Series and Linear Systems, S. Bittanti ed. Springer-Verlag, Lecture Notes in Control and Information Sciences, Vol. 86, 1986, 141–182.
Bittanti S. and P. Bolzern, Can the Kalman canonical decomposition be performed for a discrete-time linear periodic system?, 1st Latin American Conference on Automatica, Campina Grande, Brasil, 1984, 449–453.
Bittanti S. and P. Bolzern, Canonical decomposition of discrete-time linear systems, 23th Conference on Decision and Control, Las Vegas, 1984, 1984, 1737, 1738.
Bittanti S. and P. Bolzern, Four equivalent notions of stabilizability of periodic linear systems, 3rd American Control Conference, San Diego, 1984, 1321–1323.
Bittanti S. and P. Bolzern, Reachability and controllability of discrete-time linear systems, IEEE Transactions on Automatic Control, 30, 1985, 399–491.
Bittanti S. and P. Bolzern, Stabilizability and detectability of linear periodic systems, Systems and Control Letters, 6, 1985,141–145, plus Addendum, Systems and Control Letters, 7, 1985, 73.
Bittanti S. and P. Bolzern, On the structure theory of discrete-time linear systems, International Journal of Systems Sciences, 17, 1986, 33–47.
Bittanti S., P. Colaneri and G. De Nicolao, Discrete-time periodic systems: a note on the reachability and controllability interval legth, Systems and Control Letters, 8, 1986, 75–78.
Bittanti S., P. Colaneri and G. Guardabassi, H and K-controllability of linear periodic systems, 22nd Conference on Decision and Control, S. Antonio, 1983, 1376–1379.
Bittanti S., G. Guardabassi, C. Maffezzoni, and L. Silverman, Periodic systems: controllability and the matrix Riccati equation, SIAM Journal on Control and Optimization, 16, 1978, 37–40.
Bolzern P., Criteria for reachability, controllability and stabilizability of discrete-time linear periodic systems, 5th Polish-English Seminar on Real-Time Process Control, Radzjejovice, 1986, 69–83.
Brunovsky R.W., Controllability and linear closed loop controls in linear periodic systems, Journal of Differential Equations, 6, 296–313, 1969.
D’Alessandro P., A. Isidori and A. Ruberti, A new approach to the theory of canonical decomposition of linear dynamical systems, SIAM J. Control, 11, 1, 1973, 143–158.
Grasselli O.M., A canonical decomposition of linear periodic disrete-time systems, International Journal of Control, 40, 201–214, 1984.
Grasselli O.M. and S. Longhi, Sottospazi invarianti controllati e sottospazi di controllability’ per sister lineari periodici a tempo discrete, Int. Rep. 2/85, University di Ancona, 1985.
Kalman R.E., Theory of regulators for linear plants, in R.E. Kalman, P.L. Falb and M.A. Arbib: Topics in Mathematical System Theory, McGraw Hill, 1969.
Periodic Riccati Equation and Periodic Lyapunov Equation
Bekir E. and R.S. Bucy, Periodic equilibria for matrix Riccati equations, Stochastics, 2, 1976, 1–104.
Bittanti S., The Riccati equation in Control, Systems, and Signals, Lecture Notes of the IEEE/IFAC/SIAM Workshop on The Riccati Equation in Control, Systems, and Signals, Como; Pitagora Editrice, 1989.
Bittanti S., P. Bolzern and P. Colaneri, The extended periodic Lyapunov lemma, Automatica, 5, 1985, 603–605.
Bittanti S., P. Colaneri and G. De Nicolao, The periodic Riccati equation: existence of a periodic positive semidefinite solution, 26th Conference on Decision and Control, Los Angeles, 1987, 293–294.
Bittanti S., P. Colaneri and G. De Nicolao, Two techniques for the solution of the discrete-time periodic Riccati equation, in Linear Algebra in Signals, Systems and Control, B.N. Datta, C.R. Johnson, M.A. Kaashoek, R.J. Plemmons, E.D. Sontag eds., SIAM Publications, 315–331, 1988.
Bittanti S., P. Colaneri and G. De Nicolao, The difference periodic Riccati equation for the periodic prediction problem, IEEE Transactions on Automatic Control, AC — 33, 1988, 706 — 712.
Bittanti S., P. Colaneri and G. De Nicolao A note on the maximal solution of the periodic Riccati equationIEEE Transactions on Automatic Control, 34, 12, 1989, 1316–1319.
Bittanti S., P. Colaneri and G. De Nicolao, An algebraic Riccati equation for the discrete-time periodic prediction problem, Systems and Control Letters, 14, 141–182, 1990.
Bittanti S., P. Colaneri and G. De Nicolao, The periodic Riccati equation, in The Riccati Equation, S. Bittanti, A.J. Laub, J.C. Willems Eds., Springer-Verlag, 1991.
Bittanti S., P. Colaneri and G. Guardabassi, Analysis of the periodic Lyapunov and Riccati eqaution via canonical decomposition, SIAM Journal on Control and Optimization, 24, 6, 1986, 1138–1149.
Bittanti S., P. Colaneri and G. Guardabassi, Periodic solutions of periodic Ric- cati equations, IEEE Transactions on Automatic Control, 29, 7, 1984, 665–667.
Bolzern P. and P. Colaneri, Existence and uniqueness conditions for periodic solutions of the discrete-time periodic Lyapunov equation, 25th Conference on Decision and Control, Athens, 1986, 1439–1443.
Bolzern P. and P. Colaneri, The periodic Lyapunov equation, SIAM Journal on Matrix Analysis and Applications, 9, 4, 1988, 499–512.
Bucy R.S., Structural stability for the Riccati equation,SIAM Journal on Control, 13, 4, 1975, 749–761.
Da Prato G., Periodic solutions of infinite dimensional Riccati equations,Rendiconti Accademia Nazionale dei Lincei, 1984.
de Souza C.E., Riccati di f ferential equation in optimal filtering of periodic nonstabilizable systems,International Journal of Control, 46, 4, 1987, 1235–1250.
de Souza C.E., Existence conditions and properties for the maximal periodic solution of periodic Riccati difference equations, International Journal of Control, 50, 1989, 731–742.
de Souza C.E., Periodic strong solution for the optimal filtering problem of linear discrete-time periodic systems, IEEE Transactions on Automatic Control, 36, 3, 1991, 333–338.
de Souza C.E. and G.C. Goodwin, Periodic Solutions of matrix Riccati equation in optimal filtering of nonstabilizable periodic systems, IFAC World Congress, Munich, 1990, 9. 249–9. 254.
Emre E. and G. Knowles, A Newton-like approximation algoritmh for the steady-state solution of the Riccati equation for time-varying, Proceedings of the International Symposium MTNS- 85, Stockholm, 1985.
Hernandez V. and L. Jodar, Boundary problems and periodic Riccati equations, IEEE Transactions on Automatic Control, 11, 1985, 1131–1133.
Hewer G.A., Periodicity, delectability and the matrix Riccati equation,SIAM Journal of Control, 13, 6, 1235–1251, 1975.
Kano H. and T. Nishimura, Periodic solutions of matrix Riccati equations with detectability and stabilizability, International Juornal of Control, 29, 1979, 47 1487.
Kano H. and T. Nishimura, Positive-definite periodic solutions of matrix Riccati equations in continuous time,International Symposium MTNS-87.
Nishimura T and H. Kano, Periodic strong solutions of periodically time-varying matrix Riccati equations,International Journal of Control, 49, 193–205, 1989.
Shayman M.A., Varieties of invariant subspaces and the algebraic Riccati equation, Harvard University, Thesis, 1980.
Shayman M.A., On the phase portrait of the matrix Riccati equation arising from the periodic control problem,SIAM Journal on Control and Optimization, 23, 1985, 717–751.
Speyer J.L., Periodic Riccati di f ferential equation and Periodic regulator,26th Conference on Decision and Control, Los Angeles, 1987, 288–292.
Speyer J. L., The Riccati di f ferential equation and the accessory problem in the calculus of variation, in The Riccati equation in Control, Systems, and Signals, S. Bittanti ed., Pitagora Editrice, 1989, 2–8.
Identification, Signal Processing and Time Series Analysis
Bittanti S., Periodic predictors for cyclostationary processes, in Modelling, Robustness and Sensitivity Reduction in Control Systems, R. Curtain Ed., Springer-Verlag, 1987, 239–249.
Bittanti S., P. Bolzern, G. De Nicolao, L. Piroddi and D. Purassanta, A minimum prediction error algorithm for estimation of periodic ARMA models, European Control Conference, Grenoble, 1991, 1200–1203.
Bittanti S. and G. De Nicolao, Periodic ARMA models: Optimal prediction and minimum phase condition. 11th IFAC World Congress, Tallin, 1990, 96–111.
Bittanti S. and G. Guardabassi, Optimal cycling for parameter identification, 4th IFAC Symposium on Identification and System Parameter Estimation, Tblisi, 3, 1976, 590–603.
Gardner W.A., Characterization of cyclostationary random processes,IEEE Transactions on Information Theory, 21, 1, 1975, 4–14.
Gardner W. A:, Exploitation of spectral redundancy in cyclostationary signals, IEEE Signal Processing Magazine, 8, 2, 1991, 14–37.
Gardner W.A., The spectral correlation theory of cyclostationary time series,Signal Processing, 11, 1986, 13–36.
Miamee A.G. and H. Salehi, On the prediction of periodically correlated stochastic processes, in Multivariate Analysis, V.P.R. Krishnaiah ed., North Holland, 1980, 167–179.
Pagano M., Periodic and multiple autoregression,Annals of Statistics, 6, 1978, 1310–1317.
Vecchia A.V., Maximum likelihood estimation for periodic autoregressive moving average models,Technometrics, 27, 4, 1085, 375–384.
Optimal Control
Artstein Z. and A. Leizarowitz, Tracking periodic signals with the overtaking criterion, IEEE Transactions on Automatic Control, 30, 11, 1985, 1123–1126.
Bittanti S., G. Fronza, G. Guardabassi and C. Maffezzoni, A maximum priciple for periodic optimization, Ricerche di Automatica, 3, 2, 170–179, 1972.
Bittanti S., G. Fronza and G. Guardabassi, Periodic optimization of linear systems under control power constraints, Automatica, 9, 1973, 269–271.
Bittanti S., G. Fronza and G. Guardabassi, Periodic optimization of linear systems under control power constraint, Automatica, 9, 269–271, 1973.
Bittanti S. and G. Guardabassi, Optimal cyclostationary control: a parameter optimization frequency-domain approach,IFAC World Congress, Kyoto, 1981, VI-191 - VI-196.
Bittanti S. and G. Guardabassi, Optimal cyclostationary control: the LQG approach,20th IEEE Conference on Decision and Control, San Diego, 1981, 166167.
Bittanti S. and G. Guardabassi, Optimal periodic control and periodic systems analysis: a survey, 25th Conference on Decision and Control, Athens, 1986, 1417–1423.
Bittanti S., A. Locatelli and C. Maffezzoni, Second variation methods in periodic optimization, Journal of Optimization Theory and Applications, 14, 1, 1974, 3149.
Bittanti S. and C. Maffezzoni, Structural properties of a Hamiltonian system in a periodic optimization problem, Automation and Remote Control, 36, 6, Part 1, 1975, 877–884 (translated from Avtomatika i Telemekhanika, 6, 1975, 5–13 ).
Chuang C.H., J.L. Speyer and J.V. Breakwell, An asymptotic expansion about the chattering solution of an optimal periodic control problem, 26th Conference on Decision and Control, Athens, 1987.
Chuang C.H., J.L. Speyer and J.V. Breakwell, An asymptotic expansion for an optimal relaxation oscillator, SIAM Journal on Control and Optimization, 26, 3, 1988.
Colonius F., Optimality for periodic control of functional di f ferential systems. Journal of Mathematical Analysis and Applications, 1985.
Colonius F., A global maximum principle for periodic control of functional differential equations, 25th Conference on Decision and Control, Athens, 1986, 1424–1427.
Dorato P. and H.K. Knudsen, Periodic optimization with applications to solar energy control, Automatica, 15, 1979, 673–676.
Dorato P. and A.H. Levis, Optimal linear regulators: the discrete time case. IEEE Transactions on Automatic Control, 6, 613–620, 1971.
Evans R.T., Optimal periodic control theory,F.J. Seiler Research Laboratory, Air Force Systems Command, Report SRL—TR — 80 — 0024,1980.
Gilbert E.G., Optimal periodic control: A solution set theory od necessary and sufficient conditions, IFAC World Congress, Helsinki, 1978.
Gilbert E.G., Optimal periodic control: A general theory of necessary conditions. SIAM Journal on Control and Optimization, 15, 717–746, 1977.
Horn F.J.M. and R.C. Lin, Periodic Processes: A variational approach, Industrial Engineering Chemical Processes Design Devices, 5, 1, 21–30, 1967.
Maffezzoni C., Hamilton-Jacobi theory for periodic control problems,Journal of Optimization Theory and Applications, 14, 21–29, 1974.
Matsubara M., Y. Nishimura and T. Takahashi, Optimal periodic control of lumped parameter systems, Journal of Optimization Theory and Applications, 13, 1, 1974
Markus L., Optimal control of limit cycles or what control theory can do to cure a heart attack or to cause one. Symposium on Ordinary Differential Equations, Minneapolis, W.A. Harris, Y. Sibuya eds., Springer-Verlag, 1973.
Marzollo A. (ed.), Periodic optimization,Springer- Verlag, 1972.
Noldus E., A survey of optimal periodic control of continuous systems. Journal A, 16, 11–16, 1975.
Speyer J.L. and R.T. Evans, A second variational theory of optimal periodic processes, IEEE Transactions on Automatic Control, 29, 138–148, 1984.
Yakubovich V.A., Linear quadratic optimization problems and frequency theorem for periodic systems,Siberian Mathematics Journal, 27, 1986, 181–200 (Russian version in Sibirsk. Mat. Zh., 27, 4, 1986.)
Yakubovich V.A., Dichotomy and absolute stability of nonlinear systems with periodically nonstationary linear part,Systems and Control Letters, 11, 1988, 221–228.
Yakubovich V.A. and V. M. Starzhinskii, Linear differential equations with periodic coefficients, J. Wiley, 1975 (russian edition, 1972 ).
Stabilization, regulation, pole assignment and all that
Chammas A B and C.T. Leondes, On the design of linear time invariant systems by periodic output feedback, Part I and Part II, International Journal of Control, 27, 6, 1978, 885–903.
Chammas A.B. and C.T. Leondes, Pole assignment by piecewise constant output feedback, International Journal of Control, 44, 1986, 1661–1673.
Colaneri P., Zero-error regulation of discrete-time linear periodic systems,Systems and Control Letters, 15, 1990, 161–167.
Colaneri P., Output stabilization via pole placement of discrete-time linear periodic systems,IEEE Transactions on Automatic Control, AC — 36, 6, 1991, 739 —742.
Davis J. H., Stability conditions derived from spectral theory: discrete-time systems with periodic feedback, SIAM Journal of Control, 10, 1972, 1–13.
Evans M.E., Pole assignment with periodic output feedback: computer assisted study of a s-dimensional linear system,International Journal of Systems Science, 19, 12, 1988, 2661–2672.
Feintuch A., P. Khargonekar, A. Tannenbaum, On the sensistivity minimization problem for linear time-varying periodic systems, SIAM journal on Control and Optimization, 1986.
Francis B.A. and T.T. Georgiu, Stability theory for linear time invariant plants with periodic digital controllers,IEEE Transactions on Automatic Control, AC-33,9,1988,820 — 832.
Grasselli O.M. and F. Lampariello, Dead-beat control of linear periodic discrete-time systems, International Journal of Control, 33, 6, 1091–1106.
Grasselli O.M., Dead-beat observers of reduced order for linear periodic discrete-time systems with inaccessible inputs,International Journal of Control, 40, 4, 731–745, 1984.
Grasselli O.M. and S. Longhi, Disturbance localization with dead-beat control for linear periodic discrete-time systems, International Journal of Control, 44, 1986.
Grasselli O.M. and S. Longhi, Linear function dead-beat observers with disturbance localization for linear periodic discrete-time systems, International Journal of Control, 45, 1986.
Hamed M., Al- Rahmani and G.F. Franklin, Linear periodic Systems: eigenvalue assignment using discrete periodic feedback, IEEE Transactions on Automatic Control, 34, 1, 1989, 99–103.
Hernandez V. and A. Urbano, Pole-assignment problem for discrete-time linear periodic systems, International Journal of Control, 46, 2, 1987, 687–697.
Hernandez V. and A. Urbano, Pole-placenment problem for discrete-time linear periodic systems, International Journal of Control, 50, 1, 1989, 361–371.
Kabamba P.T., Monodromy eigenvalue assignment in linear periodic systems,IEEE Transactions on Automatic Control, AC — 31,1986, 950 — 952.
Kabamba P.T., Control of linear systems using generalized sampled data hold functions,IEEE Transactions on Automatic Control, AC-24,1987, 772783.
Kaczorek T., Pole placement for linear discrete-time systems by periodic output-feedbacks,Systems and Control Letters, 6, 1985.
Khargonekar P.P., K. Poola and A. Tannenbaum, Robust control of time-inveraint plants using periodic compensation, IEEE Transactions on Automatic Control, AC — 30,11,1088 — 1096, 1985.
Kern G., Linear closed-loop control in linear periodic systems with application to spin-stabilized bodies,International Journal of Control, 31, 5, 1981, 905–916.
Willems J.L., V. Kucera and P. Brunovski, On the assignment of invariant factors by time-varying strategies, Systems and Control Letters, 5, 1984, 75–80.
Periodic versus time-invariant and time varying controllers
Bailey J.E. and F.J.M. Horn, Comparison between two su f ficient conditions for improvement of an optimal steady state process by periodic operation, Journal of Optimization Theory and Applications, 7, 5, 1071.
Bernstein D.S. and E.G. Gilbert, Optimal periodic control: the H test revisited, IEEE Transactions on Automatic Control, AC — 25,673 — 684, 1980.
Bittanti S., G. Fronza and G. Guardabassi, Periodic control: a frequency domain approach, IEEE Transactions on Automatic Control, 18, 33–38, 1973.
Bittanti S., G. Fronza and G. Guardabassi, Optimal steady state versus periodic operation in discrete systems, Journal of Optimization Theory and Applications, 18, 4, 1976.
Chapellat H., M. Dahleh and S. P. Battacharrya, Structure and optimality of multivariable periodic controllers, University of California at Santa Barbara, Int. Report UCSB-ME-91–6, 1991.
Chapellat H. and M. Dahleh, Analysis of time-varying control strategies for optimal disturbance rejection and robustness, University of California at Santa Barbara, Int. Report UCSB-ME-91–9, 1991.
Colonius F., The high frequency Pi-Criterion for retarded systems. IEEE Transactions on Automatic Control, 11, 1045–1048, 1985.
Guardabassi G., Optimal steady-state versus periodic control,Ricerche di Automatica, 2, 240–252, 1971.
Guardabassi G., The optimal periodic control problem,Journal A, 17, 75–83, 1976.
Horn F.J.M. and R.C. Lin, Periodic processes: a variational approach, Industrial and Engineering Chemistry Process Design and Development, 6, 1967, 21–30.
Khargonekar P.P., K. Poola and A. Tannenbaum, Robust control of time-invaraint plants using periodic compensation, IEEE Transactions on Automatic Control, 30, 11, 1985, 1088–1096.
Watanabe N., Y. Nishimura and M. Matsubara, Singular control test for optimal periodic control problems, IEEE Transactions on Automatic Control, 1976, 609, 610.
Multirate Digital Control
Albertos P., V. Hernandez, J. Tornero and P. Morant, Block multirate input output model for continuous time linear periodic systems. IEEE Confernce on Decision and Control, 1988.
Araki M. and T. Hagiwara, Pole assignment by multirate sampled-data output feedback, International Journal of Control, 44, 1986, 1661–1673.
Al Rahmani H.M. and G.F. Franklin, A new optimal multirate control of linear periodic systems, IEEE Transactions on Automatic Control, 35, 1990, 406–415.
Berg M.C., N. Amit and J.D. Powell, Multirate digital control system design, IEEE Transactions on Automatic Control, 33, 1988, 1139–1150.
Colaneri P. and G. De Nicolao, Optimal stochastic control of multirate sampled-data systems, European Control Conference, Grenoble, 1991, 2519–2523.
Colaneri P., R. Scattolini and N. Schiavoni, The LQG problem for multirate sampled-data systems, 28th Conference on Decision and Control, Tampa, 1989, 469–474.
Colaneri P., R. Scattolini and N. Schiavoni, LQG optimal control of multirate sampled-data systems,IEEE Transactions on Automatic Control (to appear).
Colaneri P. R. Scattolini and N. Schiavoni, Stabilization of multirate sampled data systems,Automatica 26, 1990, 377–380.
Glasson D. P., A new technique for multirate digital control design and sample rate selection, Journal of Guidance, 5, 4, 1982, 379–382.
Hagiwara T. and M. Araki, Design of stable state feedback controller based on multirate sampling of the plant output, IEEE Transactions on Automatic Control, 33, 1988, 812–819.
Lennartson B., On the design of stochastic control systems with multirate sampling,Chalmers University of Technology, School of Electrical and Computer Engineering, Tech. Rep. 161, 1986.
Jury E. J., and F.J. Mullin, The analysis of sampled data control systems with a periodically time-varying sampling rate, IRE Transactions on Automatic Control, 24, 1959, 15–21.
Meyer R.A. and C.S. Burrus, A unified analysis of multirate and periodically time-varying digital filters, IEEE Transactions on Circuits and Systems, 22, 1975, 162–167.
Ritchey V.S. and G.F. Franklin, A stability criterion for asynchronous multirate linear systems, IEEE Transactions on Automatic Control, 34, 1989, 529–535.
Serrano E.J. and P.J. Ramadge, Sampled disturbace decoupling with stability using multirate control, IEEE Transactions on Automatic Control, 36, 1991, 1061–1064.
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Bittanti, S. (1992). PSICO Today. In: Isidori, A., Tarn, TJ. (eds) Systems, Models and Feedback: Theory and Applications. Progress in Systems and Control Theory, vol 12. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-2204-8_6
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