Systems-within-systems: a unifying perspective

1. Systems-within-systems:a unifying perspective Wayne J. Davis Professor Emeritus Industrial and Enterprise Systems Engineering University of Illinois@Urbana-Champaign

2. Past Future Past Future Past Future (a) (c) (b) • Physical process evolves in real time. Blue dot indicates current state, tail its observed trajectory • Process controller resides in the future. It cannot access the present: it observes immediate past as it attempts to influence the imminent future • Its planning seeks the trajectory from last observed state toward a future goal state • Often goal state corresponds to end of an assigned task

3. Past Future Past Future Past Future (a) (c) (b) (c) Multiple physical processes evolve concurrently in real time • Each process exists independently in real world • Each process has a dedicated controller that projects its future state at a common future time • These projections evolve in real time as additional observations are made

4. Past Future (d) Process controllers’ projected states at a common future time are aggregated into an initial planning state for a composite planner • Planner seeks trajectory from aggregated future state toward an assigned future goal state • Both boundary states are time-variant • The planned trajectory must be dynamic also • Planning is a process, not a task

5. Past Future (d) Continued • Planners’ response initiates from and thus contains the processes’ response • Planner relies upon processes to implement its prior plans==>planner cannot execute its plan • Processes are not subordinate to planner • Planner does not exist with its processes

6. Past Future (e) (e) Continued • Additional processes are included and aggregated to specify initial planning states for two planners • In this example, two planners share middle process • This is not a hierarchy

7. Past Future (f) (f) The two planners behave as aggregate process encapsulating the responses of their contained processes. • Another planner initializes its planning from their projected states at a common time • Aggregated processes execute this planner’s prior plans

8. Past Future (f) (f) Continued • Recursive structure is revealed • All planners behave the same

9. Past Future (f) Critical observation One: All systems have a primal and dual configurations • Primal system configuration: fix state definition and describe state evolution as function of time • Dual system configuration: Fix time and describe transitions among coupled state definitions

10. Past Future (f) Critical observation Two: Super-symmetry • Both primal and dual formulations have their dedicated primal and dual formulations • Traditional planning only considers the primal formulation of the primal configuration between two time-variant future states

11. Past Future (f) Critical observation Three: Planning is a process, not a task • Equilibration replaces optimization • Equilibration underlies energy analyses within classical mechanics

12. Major conclusion: Trajectory planning includes three components • Identifying trajectory between two future states • Collaborate with its executors to plan the initial state from which it will initialize its planning • Collaborate with planners with which its goal state is coupled For time-variant systems there are other modes of concurrent “optimizations” to be addressed collaboratively in real time.

13. Additional accomplishment: Unify classical mechanics, controls and optimization Temporally unify past and future with the present instantiates imminent future into immediate past Mathematical formulations for linear, nonlinear and discrete-event systems exist