Old research projects--but about to resurface

Aerospace

perfect winged cone-shape hypersonic vehicle

With the return to the moon (Artemis project) and more urgently the national security initiative in hypersonic technology [1], traditional aerospace control, which had been overshadowed by such more "modern" applications as Internet, power grid, biological, financial and so on control, is resurfacing with an acute sense of emergency. Artificial Interlligence, neural network control of hypersonic vehicles are likely to become prolongations of hypersonic misile design optimization by genetic algorithms as done in [1]:
  1. E. A. Jonckheere, P. Lohsoonthorn, S. Dalzell, ``Eigenstructure versus constrained H-infinity design for hypersonic winged cone,'' Journal of Guidance, Dynamics and Control, American Institute of Aeronautics and Astronautics (AIAA), Vol. 24, No., 4, pp. 648-658, July-August 2001.
  2. E. A. Jonckheere, P. Lohsoonthorn, and S. K. Bohacek, ``From Sioux City to the X-33,'' (invited paper), Annual Reviews in Control, vol. 23, Elsevier, Pergamon, 1999, pp. 91-108, 1999.
  3. E.A. Jonckheere and G.-R. Yu, ``Propulsion control of crippled aircraft by H-infinity model matching,'' IEEE Transactions on Control Systems Technology, vol. 7, pp. 142-159, March 1999.
  4. E.A. Jonckheere and G.-R. Yu,``H-infinity longitudinal control of crippled trijet aircraft with throttles only,'' invited paper, IFAC Control Engineering Practice, vol. 6, No. 5, pp. 601-613, 1998.
  5. Ph. C. Opdenacker, E.A. Jonckheere, M.G. Safonov, J.C. Juang and M. Lukich, ``Reduced order compensator design of a flexible structure," Journal of Guidance, Control and Dynamics, vol. 13, Number 1, pp. 46-56, January-February 1990.

Spectral theory of time-domain control operators

Spectrum of operator
Robust control design has traditionally been formulated in the frequency-doamin, on the premise that a stabilized control system is a frequency response to disturbances to be kept within identifiable bounds under parameter variation. Time-domain transcriptions are restricted to average or asymptotic responses. Fast switching quantum gates, more generally quantum state transfer, usually entail time-domain specifications, typically high fidelity, to be achieved within a short amount of time. Such specifications have their natural expression in the time-domain, where the achievable performance is embedded in the spectrum of Fredholm operators. This approach has its inception in the LQR problem (see [8]). This old spectral theory is promising in a new domain of applications--the spectral characterization of optimal fidelity and its variation under paramete uncertainty. 
  1. Joseph A. Ball and Edmond A. Jonckheere, ``The four-block Adamjan-Arov-Krein Problem,'' Journal of Mathematical Analysis and its Applications, Volume 170, Number 2, pp. 322-342, November 1992.
  2. E.A. Jonckheere, Jyh Ching Juang and Leonard M. Silverman, ``Spectral theory of the linear quadratic and H-infinity problems," Linear Algebra and its Applications, Special Issue on Linear Systems and Control, vol. 122-123-124, pp. 273-300, September/October/November 1989.
  3. Jyh-Ching Juang and E.A. Jonckheere, ``On computing the spectral radius of the Hankel plus Toeplitz operator," IEEE Transactions on Automatic Control, vol. AC-33, pp. 1053-1059, November 1988.
  4. E.A. Jonckheere and M. Verma, ``A spectral characterization of H-infinity optimal feedback performance and its efficient computation," Systems and Control Letters, vol. 8, pp. 13-22, October 1986.
  5. E.A. Jonckheere and L.M. Silverman, ``The linear-quadratic optimal control problem--the operator theoretic viewpoint," Operator Theory: Advances and Applications, Topics in Operator Theory Systems and Networks, vol. OT 12, Birkhauser Verlag, pp. 277-302, 1984.
  6. E.A. Jonckheere and L.M. Silverman, ``Spectral theory of the linear-quadratic optimal control problem: analytic factorization of rational matrix-valued functions," SIAM Journal on Control and Optimization, vol. 19, pp. 262-281, March 1981.
  7. E.A. Jonckheere and L.M. Silverman, ``Spectral theory of the linear-quadratic optimal control problem: a new algorithm for spectral computations," IEEE Transactions on Automatic Control, vol. AC-25, pp. 880-888, October 1980.
  8. E.A. Jonckheere and L.M. Silverman, ``Spectral theory of the linear-quadratic optimal control problem: discrete-time single-input case," IEEE Transactions on Circuits and Systems, Special Issue on Mathematical Foundation of Systems Theory, vol. CAS-25, pp. 810-825, September 1978.

Old research projects on dynamical systems, where the theory became reality--after 20 years

Dynamical systems are ubiquitous in control, aerospace, celestian mechanics, social networks, physiological systems, chaos and its various manifestations. The latter led us to consider tracking trajectories (periodic, aperiodic, transitive, etc.) within the attractor of a dynamical system with complicated (e.g., chaotic) dynamics using linear quadratic (LQ) control of the the linear systems modeling the deriation of the current trajectory from the nominal one. Such linear systems are characterized by dynamically varying (as opposed to parameter varying) systems. Hence the phraseology Linear Dynamically Varying (LDV) control. Already in [6], the possibility of using such technique in a rendez-vous with the Giaccobini-Zinner comet was considered. Given that the Trojan asteroids in the Lagrange L4 point offer a perfect example of a chaotic attractor, back in 2003, an LDV controller was theoretically designed to send a spacecraft to a rendez-vous with a Trojan asteroid [2]. Twenty years later, the Lucy spacecraft of NASA will make a flyby by the Lagrange L4 point of the Sun-Jupiter system.

Lucy

Even more recently, the James Webb telescope has been "parked" at the L2 point of the Sun-Earth system because of its (marginal) stability property. Overall, the Lagrange points offer tremendous possibilities for space exploration.



James Web L2
  1. E. Jonckheere and S. Bohacek, ``Linear Dynamically Varying (LDV) control over compact Riemannian manifolds,'' 49th IEEE Conference on Decision and Control (CDC), Atlanta, GA, December 15-17, 2010, pp. 7099-7104.
  2. F. Ariaei, E. Jonckheere and S. Bohacek, ``Tracking Trojan asteroids in periodic and quasi-periodic orbits around the Jupiter Lagrange point using LDV techniques,'' Physics and Control, St. Petersbourg, Russia, August 21-23, 2003, pp. 101--106.
  3. Stephan Bohacek and Edmond Jonckheere, ``Relationship between linear dynamically varying systems and jump linear systems,'' Mathematics of Control, Signals, and Systems(MCSS), vol. 16, pp. 207-224, 2003.
  4. S. Bohacek and E. A. Jonckheere, ``Structural stability of linear dynamically varying (LDV) controllers,'' Systems and Controls Letters (SCL), volume 44, pp. 177-187, 2001.
  5. S. Bohacek and E. A. Jonckheere, ``Nonlinear tracking over compact sets with Linear Dynamically Varying H-infinity control,'' SIAM J. Control and Optimization, vol. 40, No. 4, pp. 1042-1071, 2001.
  6. S. Bohacek and E. A. Jonckheere, ``Linear Dynamically Varying LQ control of nonlinear systems over compact sets,'' IEEE Transaction on Automatic Control, volume 46, pp. 840-852, June 2001.
  7. S. Bohacek and E. Jonckheere, "Analysis and synthesis for linear set-valued dynamically varying systems," Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334), 2000, pp. 2770-2774 vol.4, doi: 10.1109/ACC.2000.878714.

Latest news: US Space Force initiative on Security of Cis-Lunar Space

With the Artenis return-to-the-moon project and stiffening international competition for presence in cis-lunar space, securing this space has become a national priority. Navigation among the Lagrange points of the Earth-Monn system is reminiscent of our early project of navigating around the L4 point of the Jupiter-Sun system.

Cis-Lunar space