Jan Jelinek

1. Model Predictive Risk Control of Military Operations Jan Jelinek

2. Campaign Level Operational Level Task Group Level Minimal effective force compositions Task Level Threat Assessment Mission Execution Level (Tactical) Battlefield Our Focus Levels in the Command and Control Hierarchy M2PC Role: Task definition, sequencing & resource allocation Resource allocation to tasks

3. TG2 . . . . . . T11 T21 T12 T22 T2N T1N Battlefield Concept of Operations Campaign Level Operational Level . . . O Task Group Level {…,T11,T12,…,T1N,…} . . . TG1 Task Level {T11} T11(k) Mission Execution Level

4. Blue side: • Strength • Lethality • BDA quality • Red side: • Strength • Lethality • BDA quality Task Specification Slots • Objective: Destroy a Given Red Asset • = Degree of destruction <= 100% of the asset • Deadline: In 10 Missions or Less • Importance: With 95 % Certainty or Better • Own Losses: - No limit • = Victory-At-Any-Cost task formulation • - Not more than 3 strike airplanes • = Victory-With-Acceptable-Loss task formulation • Asset specs:

5. Battle dynamics as perceived by Blue Blue’s Intent Red’s Intent u(k) v(k) Red Blue Battlefield commander commander u’(k),v’(k) x(k) y(k) Blue Red BDA BDA Battle Dynamics Blue has to cope with 5 sources of uncertainty: • Battlefield (= random effects of weapons) • Red’s intent • Red commander’s strategy to fulfill the intent • Red’s Battle Damage Assessment capability • His own Battle Damage Assessment capability

6. Force-on-force Predictive Models Game-theoretic optimization Model Predictive Task Commander (MPTC) • Desired probability of win in K missions or less • Max acceptable loss • Combatants characteristics (strength, lethality, BDA) Package flying the k-th mission Monte Carlo Battle Simulator MPTC Battle Damage Assessment after the k-th mission MPC MPTC determines: • Minimal effective Blue forces for the whole sequence of missions up • to the task completion • Package composition • Sensitivity analysis

7. State distributions for the first 8 rounds / missions starting from the initial state (4,11) (read row-wise, density is proportional to probability with black being 1) Predictive Models of Battle Dynamics This information is available prior to battle and should be exploited for resource allocation and scheduling

8. B underestimates the strength of R assets Actual Red strength was systematically underestimated by 50%

9. Optimal vs. Satisficing Solutions • Military vs. mathematical requirements (e.g., target values) • A minimal effective package meeting task specifications • can be composed in many ways Offensive part of package Defensive part of package Package composition flexibility greatly complicates resource allocation

10. task variance task group variance number of tasks Resource Allocation and Task Scheduling • Averaging effect increases feasibility level • demand for resources is additive • if task are independent, then bad luck is as likely as good luck • Handling task infeasibility • Reporting it to the task order issuer • Task order issuer may delegate some of his authority to define task orders to the task group commander, e.g.: • relax importance (= probability of win) • We developed Multiple Resource Task Allocator • drop some tasks already in progress based on, e.g.: • probability of win • own losses =